# RD Sharma Solutions Chapter 5 Trigonometric Ratios Exercise 5.1 Class 10 Maths

 Chapter Name RD Sharma Chapter 5 Trigonometric Ratios Book Name RD Sharma Mathematics for Class 10 Other Exercises Exercise 5.2Exercise 5.3 Related Study NCERT Solutions for Class 10 Maths

### Exercise 5.1 Solutions

1. In each of the following one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.

Solution

2. In a Î”ABC, right angled at B, AB = 24 cm, BC = 7cm. Determine
(i) SinA, CosA
(ii) SinC, CosC
Solution
Î”ABCis right angled at B
AB = 24cm, BC = 7cm.

3. In Fig below, Find tan P and cot R. Is tan P = cot R?
Solution

4. If sin A = 9/41,  compute cosA and tanA
Solution

5.Given 15 cotA = 8, find Sin A and secA.
Solution

15 cot A = 8, find Sin A and sec A

6. In Î”PQR, 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

Î”PQR, right angled at Q.

7. If cot Î¸ =7/8, evaluate :
(i) [(1 + sinÎ¸)(1 - sinÎ¸)]/[(1 + cosÎ¸)(1 - cosÎ¸)
(ii) Cot2Î¸
Solution

8. If 3cotA = 4, check whether (1 - tan2A)/(1 + tan2A) = cos2A - sin2A or not.
Solution

9. If tan Î¸ = a/b, find the value of (cosÎ¸ + sinÎ¸)/(cosÎ¸ - sinÎ¸).
Solution

10. If 3 tanÎ¸ = 4, find the value of (4cosÎ¸ - sinÎ¸)/(2cosÎ¸ + sinÎ¸).
Solution

11. If 3cotÎ¸ = 2, find the value of = (4sinÎ¸ - 3cosÎ¸)/(2sinÎ¸ + 6sinÎ¸)
Solution

12. If tanÎ¸ = a/b, prove that (a sinÎ¸ - b cosÎ¸)/(a sinÎ¸ + b cosÎ¸) = (a2 - b2)/(a2 + b2).
Solution

13. If secÎ¸ = 13/5, show that (2cosÎ¸ - 3cosÎ¸)/(4sinÎ¸ - 9cosÎ¸) = 3
Solution

14. If cosÎ¸ = 12/13, show that sinÎ¸ (1 - tanÎ¸) = 35/156 .
Solution

15. If cotÎ¸ = 1/√3, show that  (1 - cos2Î¸)/(2 - sin2Î¸) = 3/5 .
Solution

16. If tanÎ¸ = 1/√7
(cosec2Î¸  - sec2Î¸)/(cosec2Î¸ + sec2Î¸) = 3/4
Solution

17. If SinÎ¸ = 12/13 find (sin2Î¸ - cos2Î¸)/(2 sinÎ¸ cosÎ¸) × 1/tan2Î¸
Solution

18.  If secÎ¸ = 5/4 , find the value of (sinÎ¸ - 2cosÎ¸)/(tanÎ¸ - cotÎ¸)
Solution

19. TanÎ¸ = 12/13
Find (2sinÎ¸ cosÎ¸)/(cos2Î¸ - sin2Î¸)
Solution

21. If cosÎ¸ = 3/5, find the value of  (sinÎ¸ - 1/tanÎ¸)/2tanÎ¸ .
Solution

22. If sinÎ¸ = 3/5, evaluate  (cosÎ¸ - 1/tanÎ¸)/2cotÎ¸
Solution

23. If sec A = 5/4, verify that (3sinA - 4sin3A)/(4cos3A - 3cos A) = (3tanA - tan3A)/(1 - 3tan2A).
Solution

24. If sec A = 17/8, verify that (3 - 4sin2A)/(4cos2A - 3) = (3 - tan2A)/(1 - 3tan2A)
Solution

25. If cot Î¸ = 3/4, prove that √(secÎ¸ - cosecÎ¸)/(secÎ¸ + cosecÎ¸) = 1/√7
Solution

27. If tanÎ¸Î¸ = 24/7, find that sin Î¸ + cos Î¸
Solution

28. If sin Î¸ = a/b, find sec Î¸ + tanÎ¸ in terms of a and b.
Solution

29.  If 8 tan A = 15, find  sinA - cosA.
Solution

30. If 3cosÎ¸ - 4sinÎ¸ = 2cosÎ¸ + sinÎ¸ Find tanÎ¸ .
Solution

3cosÎ¸ - 2cosÎ¸ = 4sinÎ¸ + sinÎ¸ find tanÎ¸
3cosÎ¸ - 2cosÎ¸ = sinÎ¸ + 4sinÎ¸
cosÎ¸ = 5sinÎ¸
Dividing both side by use we get
cosÎ¸/cosÎ¸ = 5sinÎ¸/cosÎ¸
1 = 5tanÎ¸
⇒ tanÎ¸ = 1

31.  If tanÎ¸ = 20/21, show that (1- sinÎ¸ + cosÎ¸)/(1 + sinÎ¸ + cosÎ¸) = 3/7
Solution

32. If Cosec A = 2 find 1/tanA + sinA/(1 + cosA)
Solution

33. If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
Solution

34. If ∠A and ∠P are acute angles such that tan A = tan P, then show that ∠A = ∠P.
Solution

A and P are acute angle tan A = tan P
S.T.     ∠A = ∠P
Let us consider right angled triangle ACP,

35. In a Î”ABC, right angled at A, if tan C = √3, find the value of sin B cos C + cos B sin C .
Solution
In a Î”le  ABC right angled at A tan C = √3
Find sin B cos C + cos B sin C

36. State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than I.
(ii)  Sec A = 12/5 for some value of angle A.
(iii) Cos A is the abbreviation used for the cosecant of angle A.
(iv) Sin Î¸ = 4/3 for some angle Î¸.
Solution

(a) Tan A ∠1
Value of tan A at 45° i.e., tan 45 = 1
As value of A increases to 90°
Tan A becomes infinite
So given statement is false.

(b) Sec A = 12/5 for some value of angle of
M - I
Sec A = 2.4
Sec A > 1
So given statement is True
M - II
For sec A = 12/5
For sec A = 12/5 we get adjacent side = 13

We get a right angle Î”le
Subtending 9i at B.
So, given statement is true.
(c)  Cos A is the abbreviation used for cosecant of angle A.
The given statement is false
∴ Cos A is abbreviation used for cos of angle A but not for cosecant of angle A.
(d) Cot A is the product of cot A and A
Given statement is false
∵ cot A is co - tangent of angle A and co - tangent of angle A = (adjacent side)/(opposite side)
(e)  Sin Î¸ = 4/3  for some angle Î¸
Given statement is false
Since value of sin Î¸ is less than (or) equal to one. Here value of sin Î¸ exceeds one, so given statement is false.