Q. sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x

1.	Q. sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x
Answer» ong>ANSWER: ANSWER 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.

Answer»

ong>ANSWER:

ANSWER

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.

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Q. sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x​

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Q. sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x