For x not a multiple of 2π, prove by induction that cos x+ 2x+·s+cos nx= cos (n+1)x 2 ,sin nx 2 sin x2.

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[JEE Advanced 1994] for x not a multiple of 2 pi prove by induction that cos x

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For $x$ not a multiple of $2\pi$, prove by induction that $\cos x+\cos2x+\cdots+\cos nx=\dfrac{\cos\frac{(n+1)x}2\,\sin\frac{nx}2}{\sin\frac x2}$.

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Answer: Proved.

Base $n=1$ holds; the step adds $\cos(n+1)x$ and uses product-to-sum identities, advancing the closed form from $n$ to $n+1$.

JEE Advanced 1994 · Binomial Theorem — verified solution by the Vidaara Team.

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