Question

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

Answer 1

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Answer 2

$\large{\red{\mathfrak{solution}}$

{ This types of question you should either proved LHS or RHS }

L.H.S.

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

= cos (n + 1)x cos (n + 2)x + sin (n + 1)x × sin (n + 2)x

[Formula cos (x – y) – cos x cos y + sin x sin y]

= cos [(n + 1)x – (n + 2)x]

= cos [nx + x – nx – 2x]

= cos (- x) cos x = R.H.S.

Hence Proved