NCERT solution class 11 chapter 3 Trigonometric Functions exercise 3.5 mathematics

EXERCISE 3.5

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Page No 81:

Question 1:

Prove that: 

Answer:

L.H.S.

= 0 = R.H.S

Question 2:

Prove that: (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0

Answer:

L.H.S.
= (sin 3x + sin x) sin x + (cos 3x – 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 6x
= 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, cosx 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.

 [cosx is negative in quadrant II]




Thus, the respective values of are .

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