CBSE Class 10

RS Aggarwal Solutions Class 10 Chapter 5 Trigonometric Ratios Ex 5

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 5 Trigonometric Ratios Ex 5.

Other Exercises

• RS Aggarwal Solutions Class 10 Chapter 5 Trigonometric Ratios Ex 5

Question 1.
Solution:

Question 2.
Solution:

Question 3.
Solution:

Question 4.
Solution:

Question 5.
Solution:

Question 6.
Solution:

Question 7.
Solution:

Question 8.
Solution:

Question 9.
Solution:

Question 10.
Solution:

Question 11.
Solution:

Question 12.
Solution:

Question 13.
Solution:

Question 14.
Solution:

Question 15.
Solution:

Question 16.
Solution:

Question 17.
Solution:

Question 18.
Solution:

Question 19.
Solution:

Question 20.
Solution:

Question 21.
Solution:

Question 22.
Solution:

Question 23.
Solution:

Question 24.
Solution:

Question 25.
Solution:

Question 26.
Solution:

Question 27.
Solution:

Question 28.
Solution:

Question 29.
Solution:

Question 30.
Solution:
Consider two right triangles XAY and WBZ such that sin A = sin B

Question 31.
Solution:
Consider two right triangles XAY and WBZ such that tan A = tan B

Question 32.
Solution:

Question 33.
Solution:

Question 34.
Solution:

Question 35.
Solution:

We hope the RS Aggarwal Solutions Class 10 Chapter 5 Trigonometric Ratios Ex 5 help you. If you have any query regarding RS Aggarwal Solutions Class 10 Chapter 5 Trigonometric Ratios Ex 5, drop a comment below and we will get back to you at the earliest.

RS Aggarwal Solutions Class 10 Chapter 6 T-Ratios of Some Particular Angles Ex 6

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 6 T-Ratios of Some Particular Angles Ex 6.

Other Exercises

• RS Aggarwal Solutions Class 10 Chapter 6 T-Ratios of Some Particular Angles Ex 6

Question 1.
Solution:
On substituting the value of various T-ratios, we get
sin60° cos30° + cos60° sin30°

Question 2.
Solution:
On substituting the value of various T-ratios, we get
cos60° cos30° – sin60° sin30°

Question 3.
Solution:
On substituting the value of various Tratios, we get
cos45° cos30° + sin45° sin30°

Question 4.
Solution:
On substituting the value of various Tratios, we get

Question 5.
Solution:

Question 6.
Solution:
On substituting the value of various Tratios, we get

Question 7.
Solution:
On substituting the value of various Tratios, we get

Question 8.
Solution:
On substituting the value of various Tratios, we get

Question 9.
Solution:
On substituting the value of various Tratios, we get

Question 10.
Solution:
(i)

(ii)

Question 11.
Solution:
(i)

R.H.S. = L.H.S.
Hence, sin60° cos30° – cos60° sin30° = sin30°

(ii)
L.H.S. = cos60° cos30° + sin60° sin30°

(iii)

R.H.S. = L.H.S.
Hence,2sin30° cos30° = sin60°

(iv)

R.H.S. = sin90° = 1
R.H.S. = L.H.S.
Hence, 2 sin 45° cos45° = sin90°

Question 12.
Solution:
A = 45° 2 A = 90°

(i)Sin 2A = sin90° = 1

(ii) cos2A = cos90° = 0

Question 13.
Solution:
A = 30 ⇒ 2A = 60

(i)

(ii)

(iii)

Question 14.
Solution:
(i)

(ii)

Question 15.
Solution:
(i)

(ii)

(iii)

Question 16.
Solution:

Hence, (A + B) = 45

Question 17.
Solution:
Putting A = 30° 2 A = 60°

Question 18.
Solution:
Putting A = 30° 2 A = 60°

Question 19.
Solution:
Putting A = 30° 2 A = 60°

Question 20.
Solution:
From right angled ∆ABC,

Question 21.
Solution:
From right angled ∆ABC,

Question 22.
Solution:
From right angled  ∆ABC,

(i)

(ii)
By Pythagoras theorem

Hence, (i) BC = 3cm and (ii) AB = 3cm.

Question 23.
Solution:
sin (A + B)= 1  sin (A + B) = sin90°

Adding (1) and (2), we get
2A = 90° ⇒ A = 45°
Putting A = 45° in (1) we get
45° + B = 90° ⇒ B = 45°
Hence, A = 45° and B = 45°.

Question 24.
Solution:

Solving (1) and (2), we get
2A = 90° ⇒ A = 45°
Putting A = 45° in (1), we get
45° – B = 30° ⇒ B = 45 – 30° = 15°
Hence, A = 45°, B = 15°.

Question 25.
Solution:

Solving (1) and (2), we get
2A = 90° ⇒ A = 45°
Putting A = 45° in (1), we get
45° – B = 30° ⇒ B = 45° – 30°  = 15°
A = 45°, B = 15°

Question 26.
Solution:

Question 27.
Solution:

We hope the RS Aggarwal Solutions Class 10 Chapter 6 T-Ratios of Some Particular Angles Ex 6 help you. If you have any query regarding RS Aggarwal Solutions Class 10 Chapter 6 T-Ratios of Some Particular Angles Ex 6, drop a comment below and we will get back to you at the earliest.

RS Aggarwal Solutions Class 10 Chapter 7 Trigonometric Ratios of Complementary Angles Ex 7

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 7 Trigonometric Ratios of Complementary Angles Ex 7.

Other Exercises

• RS Aggarwal Solutions Class 10 Chapter 7 Trigonometric Ratios of Complementary Angles Ex 7

Question 1.
Solution:
(i)

(ii)

(iii)

(iv)

(v)

(vi)

Question 2.
Solution:
(i)  LHS = cos81° – sin9°
= cos(90° -9°)- sin9° = sin9° – sin9°
= 0 = RHS

(ii) LHS = tan71° – cot19°
=tan(90° – 19°) – cot19° =cot19° – cot19°
=0 = RHS

(iii) LHS = cosec80° – sec10°
= cosec(90° – 10°) – sec(10°)
= sec10° – sec10° = 0
= RHS

(iv) LHS = cosec² 72° − tan² 18°

(v) LHS = cos² 75° + cos² 15°

(vi) LHS = tan² 66° − cot² 24°

(vii) LHS = sin² 48° + sin² 42°

(viii) LHS = cos² 57° − sin² 33°

(ix) LHS = (sin 65° + cos 25°)(sin 65° − cos 25°)

Question 3.
Solution:
(i)

(ii)

(iii)

(iv)

(v)

(vi)

Question 4.
Solution:
(i)

(ii)

(iii)

(iv)

(v)

Question 5.
Solution:
(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

Question 6.
Solution:
(i)

(ii)

(iii)

(iv)

(v)

Question 7.
Solution:
(i)  LHS = sin (70° + θ) − cos (20° − θ)

(ii)  LHS = tan (55° − θ) − cot (35° + θ)

(iii)  LHS = cosec (67° + θ) − sec (23° − θ)

(iv)  LHS = cosec (65 °+ θ)  sec  (25° −  θ) − tan (55° − θ) + cot (35° + θ)

(v)  LHS = sin (50° + θ ) − cos (40° − θ) + tan 1° tan 10° tan 80° tan 89°

Question 8.
Solution:
(i)

(ii)

(iii)

(iv)

Question 9.
Solution:

Question 10.
Solution:

Question 11.
Solution:

Question 12.
Solution:

Question 13.
Solution:

Question 14.
Solution:

Question 15.
Solution:

We hope the RS Aggarwal Solutions Class 10 Chapter 7  Trigonometric Ratios of Complementary Angles Ex 7 help you. If you have any query regarding RS Aggarwal Solutions Class 10 Chapter 7  Trigonometric Ratios of Complementary Angles Ex 7, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 10 Social Science Civics Chapter 2 Federalism

These Solutions are part of NCERT Solutions for Class 10 Social Science. Here we have given NCERT Solutions for Class 10 Social Science Civics Chapter 2 Federalism.

TEXTBOOK EXERCISES

Question 1.
Locate the following States on a blank outline political map of India: Manipur, Sikkim, Chhattisgarh, and Goa.
Answer:
The states have been shown in the map on page P – 15.

Question 2.
Identify and shade three federal countries (other than India) on a blank outline political map of the world.
Answer:
Federal states — USA, Brazil, and Australia have been shown in the map on page P-16.

Question 3.
Point out one feature in the practice of federalism in India that is similar to and one feature that is different from that of Belgium.
Answer:
(1) Similar features: Distribution of powers –

In both the countries, power has been divided among the national government, state (provincial) government, and local governments (community govt, in Belgium).

• In Belgium,
  1. The regional governments have jurisdiction over transportation, public works, water policy, education, public health, and housing, etc.
  2. The community government has the power regarding cultural, educational, and language-related issues.
• In India, for example
  1. The legislative powers have been divided between the Union Govt and the State Governments.
  2. It contains three lists – Union list, State list, and Concurrent list.
  3. By the Act of 1992, the third tier e., local govts, have been granted more powers.

(2) Different features: Forms of government – In Belgium in addition to Central and State government, there is a third kind of government that is community government. This is elected by people belonging to one language community – Dutch, French, and German-speaking – no matter where they live. This government deals with cultural, educational, and language-related issues. In India, there is no such government.

In India, there is a three-tier government. The third government is the local government i.e., Panchayats at the village level and Municipalities at the town level. These bodies have been given powers by constitutional amendment in 1992.
Some of the provisions of the Act are as mentioned below :

• Mandatory to hold regular elections to local govt, bodies.
• Reservation of seats for SC/ST/OBC.
• Reservation of 1/3 seats for women.
• State Election Commission to hold elections.
• State govt, to share some powers.

Question 4.
What is the main difference between a federal form of government and a unitary one? Explain with an example.
Answer:
Under the federal system, generally, there are two sets of government i.e., national and state. Powers are divided between the two. For example in India, there are three lists – Union list, State list, and Concurrent list. The central or national government makes laws on the subjects in the Union List. These are subjects of national importance such as defense, foreign affairs and currency.

The state governments enact laws on the subjects included in the state list. These subjects are of state and local importance such as police, trade, agriculture and irrigation. Both the governments can enact laws on the subjects included in the concurrent list which includes subjects of common interest. These are education, forest, trade unions, and marriage etc.

On the other hand, under the unitary system, there is only one level of government at the national level. There are no provincial or state governments as we have in India. There is, therefore, no division of powers. The units or provincial government if any, are subordinate to the central government or national government as in England. The central or national government has all the powers.

Question 5.
State any two differences between the local government before and after the Constitutional amendment in 1992.                                                                                      ,
Answer:
A major step towards decentralization was taken in 1992. The Constitution was amended to make the third-tier of democracy more powerful and effective. Now it is constitutionally mandated to hold regular elections to local government bodies. Seats are reserved in the elected bodies and the executive heads of these institutions for the Scheduled Castes, Scheduled Tribes and Other Backward Classes.

At least one-third of all positions are reserved for women. An independent institution called the State Election Commission has been created in each State to conduct panchayat and municipal elections. The State governments are required to share some powers and revenue with local government bodies. The nature of sharing varies from State to State.

Question 6.
Fill in the blanks :

Since the United States is a (1)_________________________ type of federation, all the Constituent States have equal powers and States are (2)________________________ vis-a-vis the federal government. But India is a (3)_____________________ type of federation and some States have more power than others. In India, the (4)_______________________ govern­ment has more powers.
Answer:
(1) coming together (2) strong (3) holding together (4) central

Question 7.
Here are three reactions to the language policy followed in India. Give an argument and an example to support any of these positions.
Sangeeta: The policy of accommodation has strengthened national unity.
Arman: The language-based States have divided us by making everyone con­scious of their language.
Harish: This policy has only helped to consolidate the dominance of English over all other languages.
Answer:
The position held by Sangeeta that the policy of accommodation has strengthened national unity is correct. The Central Government agreed to continue the use of English along with Hindi for official purposes to avoid the Lankan kind of situation. Otherwise, the move­ment against Hindi would have taken a more ugly turn. The promotion of Hindi continues to be the official policy of the Government of India. Promotion does not mean that the Central Government can impose Hindi on states where people speak a different language. The flexibility shown by our leaders helped our country avoid the kind of situation that Sri Lanka finds itself in. Thus the policy of accommodation has strengthened national unity. Hindi is being used along with English for official purposes.

Question 8.
The distinguishing feature of a federal government is :
(a) National government gives some powers to the provincial government.
(b) Power is distributed among the legislature, executive, and judiciary.
(c) Elected officials exercise supreme power in the government.
(d) Governmental power is divided between different levels of government.

Question 9.
A few subjects in various Lists of the Indian Constitution are given here. Group them under the Union, State, and Concurrent Lists as provided in the table below :
Defence; B. Police; C. Agriculture; D. Education; E. Banking; F. Forests;  G. Communications; H. Trade; I. Marriages.

Answer:

1. Union List: Defence, Banking and Communications.
2. State List: Police, Agriculture and Trade.
3. Concurrent List; Education, Forests and Marriages.

Question 10.
Examine the following pairs that give the level of government in India and the powers of the government at that level to make laws on the subjects mentioned against each. Which of the following pairs is not correctly matched ?

Answer:
(d) Local governments — Residuary powers. It is not correctly matched because the residuary powers have been given to the Central Government.

Question 11.
Match List I with List-II and select the correct answer using the codes given below the lists :

Answer:
(c) A, C, D, B.

Question 12.
Consider the following statements:

(a) In a federation, the powers of the federal and provincial governments are clearly demarcated.

(b) India is a federation because the powers of the Union and State Govern­ments are specified in the Constitution and they have exclusive jurisdiction on their respective subjects.

(c) Sri Lanka is a federation because the country is divided into provinces.

(d) India is no longer a federation because some powers of the States have been devolved to the local government bodies.

Which of the statements given above are correct?
(a) A, B, and C
(b) A, C, and D
(c) A and B only
(d) B and C only

We hope the NCERT Solutions for Class 10 Social Science Civics Chapter 2 Federalism help you. If you have any query regarding Extra Questions for Class 10 Social Science Civics Chapter 1 Power Sharing, drop a comment below and we will get back to you at the earliest.

RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Test Yourself

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Test Yourself.

Other Exercises

• RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Ex 8a
• RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Ex 8b
• RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Ex 8c
• RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities MCQ
• RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Test Yourself

Question 1.
Solution:

Question 2.
Solution:

Question 3.
Solution:

Question 4.
Solution:

Question 5.
Solution:

Question 6.
Solution:

Question 7.
Solution:

Question 8.
Solution:

Question 9.
Solution:

Question 10.
Solution:

Question 11.
Solution:

Question 12.
Solution:

Question 13.
Solution:

Question 14.
Solution:

Question 15.
Solution:

Question 16.
Solution:

Question 17.
Solution:

Question 18.
Solution:

Question 19.
Solution:

Question 20.
Solution:

We hope the RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Test Yourself help you. If you have any query regarding RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Test Yourself, drop a comment below and we will get back to you at the earliest.