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Question

Prove the following:
sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

Solution
Verified by Toppr

Use cosAcosB+sinAsinB=cos(AB)

LHS=sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cos[(n+2)x(n+1)x]

=cosx=RHS

Hence proved.

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