## NCERT Solutions for Class 11 Maths Chapter 3 – Trigonometric Functions Miscellaneous Exercise

#### Page No 81:

#### Question 1:

Prove that:

#### Answer:

L.H.S.

= 0 = R.H.S

#### Question 2:

Prove that: (sin 3

*x*+ sin*x*) sin*x*+ (cos 3*x*– cos*x*) cos*x*= 0#### Answer:

L.H.S.

= (sin 3

*x*+ sin*x*) sin*x*+ (cos 3*x*– cos*x*) cos*x*
= RH.S.

#### Page No 82:

#### Question 3:

Prove that:

#### Answer:

L.H.S. =

#### Question 4:

Prove that:

#### Answer:

L.H.S. =

#### Question 5:

Prove that:

#### Answer:

It is known that.

∴L.H.S. =

#### Question 6:

Prove that:

#### Answer:

It is known that

.

L.H.S. =

= tan 6

*x*
= R.H.S.

#### Question 7:

Prove that:

#### Answer:

L.H.S. =

#### Question 8:

,

*x*in quadrant II#### Answer:

Here,

*x*is in quadrant II.
i.e.,

Therefore, are all positive.

As

*x*is in quadrant II, cos*x*is negative.
∴

Thus, the respective values of are.

#### Question 9:

Find for ,

*x*in quadrant III#### Answer:

Here,

*x*is in quadrant III.
Therefore, and are negative, whereasis positive.

Now,

Thus, the respective values of are.

#### Question 10:

Find for ,

*x*in quadrant II#### Answer:

Here,

*x*is in quadrant II.
Therefore,, and are all positive.

[cos

*x*is negative in quadrant II]
Thus, the respective values of are .

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