RD Sharma Class 11 Solutions Chapter - Values of Trigonometric Functions

 Page 1


9. Values of Trigonometric Functions at Multiples and
Submultiple of an Angles
Exercise 9.1
1. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = 1 – 2 sin
2
 x
= 2cos
2
 x – 1
Therefore,
= tan x
= RHS
Hence Proved
2. Question
Prove the following identities:
Page 2


9. Values of Trigonometric Functions at Multiples and
Submultiple of an Angles
Exercise 9.1
1. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = 1 – 2 sin
2
 x
= 2cos
2
 x – 1
Therefore,
= tan x
= RHS
Hence Proved
2. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = 1 – 2 sin
2
 x
sin 2x = 2 sin x cos x
Therefore,
= cot x
= RHS
Hence Proved
3. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = 2 cos
2
 x – 1
sin 2x = 2 sin x cos x
Page 3


9. Values of Trigonometric Functions at Multiples and
Submultiple of an Angles
Exercise 9.1
1. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = 1 – 2 sin
2
 x
= 2cos
2
 x – 1
Therefore,
= tan x
= RHS
Hence Proved
2. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = 1 – 2 sin
2
 x
sin 2x = 2 sin x cos x
Therefore,
= cot x
= RHS
Hence Proved
3. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = 2 cos
2
 x – 1
sin 2x = 2 sin x cos x
Therefore,
= tan x
= RHS
Hence Proved
4. Question
Prove the following identities:
Answer
Proof:
Take LHS:
{? cos 2x = 2 cos
2
 x – 1 ? cos 4x = 2 cos
2
 2x -1}
{? cos 2x = 2 cos
2
 x – 1}
= 2 cos x
= RHS
Page 4


9. Values of Trigonometric Functions at Multiples and
Submultiple of an Angles
Exercise 9.1
1. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = 1 – 2 sin
2
 x
= 2cos
2
 x – 1
Therefore,
= tan x
= RHS
Hence Proved
2. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = 1 – 2 sin
2
 x
sin 2x = 2 sin x cos x
Therefore,
= cot x
= RHS
Hence Proved
3. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = 2 cos
2
 x – 1
sin 2x = 2 sin x cos x
Therefore,
= tan x
= RHS
Hence Proved
4. Question
Prove the following identities:
Answer
Proof:
Take LHS:
{? cos 2x = 2 cos
2
 x – 1 ? cos 4x = 2 cos
2
 2x -1}
{? cos 2x = 2 cos
2
 x – 1}
= 2 cos x
= RHS
Hence Proved
5. Question
Prove the following identities:
Answer
Proof:
Take LHS
Identities used:
cos 2x = 2 cos
2
 x – 1
= 1 – 2 sin
2
 x
sin 2x = 2 sin x cos x
Therefore,
= tan x
= RHS
Hence Proved
6. Question
Prove the following identities:
Answer
Page 5


9. Values of Trigonometric Functions at Multiples and
Submultiple of an Angles
Exercise 9.1
1. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = 1 – 2 sin
2
 x
= 2cos
2
 x – 1
Therefore,
= tan x
= RHS
Hence Proved
2. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = 1 – 2 sin
2
 x
sin 2x = 2 sin x cos x
Therefore,
= cot x
= RHS
Hence Proved
3. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = 2 cos
2
 x – 1
sin 2x = 2 sin x cos x
Therefore,
= tan x
= RHS
Hence Proved
4. Question
Prove the following identities:
Answer
Proof:
Take LHS:
{? cos 2x = 2 cos
2
 x – 1 ? cos 4x = 2 cos
2
 2x -1}
{? cos 2x = 2 cos
2
 x – 1}
= 2 cos x
= RHS
Hence Proved
5. Question
Prove the following identities:
Answer
Proof:
Take LHS
Identities used:
cos 2x = 2 cos
2
 x – 1
= 1 – 2 sin
2
 x
sin 2x = 2 sin x cos x
Therefore,
= tan x
= RHS
Hence Proved
6. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = cos
2
 x – sin
2
 x
sin 2x = 2 sin x cos x
Therefore,
= tan x
= RHS
Hence Proved
7. Question
Prove the following identities:
Answer
Proof:
Take LHS:
Identities used:
cos 2x = cos
2
 x – sin
2
 x
sin 2x = 2 sin x cos x
Therefore,