[JEE Advanced 1994] For $x$ not a multiple of $2\pi$, prove by induction that $\cos x+\cos2x+\cdots+\cos nx=\dfrac{\cos\frac{(n+1)x}2\,\sin\frac{nx}2}{\sin\frac x2}$.
For $x$ not a multiple of $2\pi$, prove by induction that $\cos x+\cos2x+\cdots+\cos nx=\dfrac{\cos\frac{(n+1)x}2\,\sin\frac{nx}2}{\sin\frac x2}$.
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VAVidaara Admin
✓ Vidaara Team
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· 1mo ago
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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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