RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1

RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1

Other Exercises

Question 1.
In each of the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 1
Solution:
∴ Perpendicular BC – 2 units and
Hypotenuse AC = 3 units
By Phythagoras Theorem, in AABC,
(Hypotenuse)2 = (Base)2 + (Perpendicular)2
AC2 = AB2 + BC2
⇒ (3)2 = (AB)2 + (2)2
⇒ 9 = AB2 + 4 ⇒ AB2 = 9-4 = 5
AB = √5 units
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Question 2.
In a ΔABC, right angled at B, AB = 24 cm, BC = 7 cm. Determine
(i) sin A, cos A
(ii) sin C, cos C.

Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 21

Question 3.
In the figure, find tan P and cot R. Is tan P = cot R ?
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 22
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 23

Question 4.
If sin A = \(\frac { 9 }{ 41 }\), compute cos A and tan A.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 24

Question 5.
Given 15 cot A = 8, find sin A and sec A.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 25

Question 6.
In ΔPQR, right angled at Q, PQ = 4 cm and RQ = 3 cm. Find the values of sin P, sin R, sec P and sec R.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 26
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Question 7.
If cot 0 = \(\frac { 7 }{ 8 }\), evaluate :
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Solution:
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Question 8.
If 3 cot A = 4, check whether \(\frac { 1-{ tan }^{ 2 }A }{ 1+{ tan }^{ 2 }A }\) = cos2 A – sin2 A or not.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 32
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Question 9.
If tan θ = a/b , Find the Value of \(\frac { cos\theta +sin\theta }{ cos\theta -sin\theta }\).
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 34
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 35

Question 10.
If 3 tan θ = 4, find the value of 4cos θ – sin θ \(\frac { 4cos\theta -sin\theta }{ 2cos\theta +sin\theta }\).
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 36
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Question 11.
If 3 cot 0 = 2, find the value of \(\frac { 4sins\theta -3cos\theta }{ 2sin\theta +6cos\theta }\).
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 38

Question 12.
If tan θ = \(\frac { a }{ b }\), prove that
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Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 40

Question 13.
If sec θ = \(\frac { 13 }{ 5 }\), show that \(\frac { 2sins\theta -3cos\theta }{ 4sin\theta -9cos\theta }\) =3.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 41

Question 14.
If cos θ \(\frac { 12 }{ 13 }\), show that sin θ (1 – tan θ) \(\frac { 35 }{ 156 }\).
Solution:
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Question 15.
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Solution:
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Question 16.
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Solution:
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Question 17.
If sec θ = \(\frac { 5 }{ 4 }\), find the value of \(\frac { sins\theta -2cos\theta }{ tan\theta -cot\theta }\).
Solution:
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Question 18.
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Solution:
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Question 19.
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Solution:
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Question 20.
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Solution:
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Question 21.
If tan θ = \(\frac { 24 }{ 7 }\), find that sin θ + cos θ.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 61
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Question 22.
If sin θ = \(\frac { a }{ b }\), find sec θ + tan θ in terms of a and b.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 63

Question 23.
If 8 tan A = 15, find sin A – cos A.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 64

Question 24.
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Solution:
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Question 25.
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Solution:
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Question 26.
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
Solution:
∠A and ∠B are acute angles and cos A = cos B
Draw a right angle AABC, in which ∠C – 90°
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Question 27.
In a ∆ABC, right angled at A, if tan C =√3 , find the value of sin B cos C + cos B sin C. (C.B.S.E. 2008)
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 72
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 73

Question 28.
28. State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) sec A = \(\frac { 12 }{ 5 }\) for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) sin θ = \(\frac { 4 }{ 3 }\) for some angle θ.
Solution:
(i) False, value of tan A 0 to infinity.
(ii) True.
(iii) False, cos A is the abbreviation of cosine A.
(iv) False, it is the cotengent of angle A.
(v) Flase, value of sin θ varies on 0 to 1.

Question 29.
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Solution:
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Question 30.
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Solution:
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Question 31.
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Solution:
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Question 32.
If sin θ =\(\frac { 3 }{ 4 }\), prove that
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Solution:
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Question 33.
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Solution:
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Question 34.
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Solution:
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Question 35.
If 3 cos θ-4 sin θ = 2 cos θ + sin θ, find tan θ.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 94

Question 36.
If ∠A and ∠P are acute angles such that tan A = tan P, then show that ∠A = ∠P.
Solution:
∠A and ∠P are acute angles and tan A = tan P Draw a right angled AAPB in which ∠B = 90°
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.1 95

 

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