Question

Select the correct option from the given alternatives :

The value of sin(n + 1) A sin (n + 2) A + cos(n + 1) A cos(n + 2) A is equal to

Options

• sin A 

• cos A

• – cos A

• sin 2A

Answer 1

cos A

Explanation:

L.H.S. = sin [(n + 1)A] . sin [(n + 2)A] + cos [(n + 1)A] . cos [(n + 2)A]

= cos [(n + 2)A] . cos [(n + 1)A] + sin [(n + 2)A] . sin [(n + 1)A]

Let (n + 2)A = a and (n + 1)A = b …(i)

∴ L.H.S. = cos a . cos b + sin a . sin b
= cos (a − b)
= cos [(n + 2)A − (n + 1)A] ........[From (i)]
= cos [(n + 2 − n − 1)A]
= cos A
= R.H.S.