Question

ii) The value of sin (n+1) A sin(n+2) A + cos (n+1) A cos (n+2)A is equal to
a) sin A b) cos A c) -COS A
d) sin2A​

Answer 1

Answer:

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Step-by-step explanation:

To prove:- sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

Proof :−

L.H.S.=

sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x

=cos((n+2)x−(n−1)x){∵cos(A−B)=sinAsinB+cosAcosB}

⇒=cos((n+2−n−1)x)

⇒=cosx=R.H.S.

Hence proved.