NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

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.

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, whereas  is 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   .