If `f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)ddot(cosn x+isinn x)` and `f(1)=1` , then `f"(1)` is equal to `(n(n+1))/2` (b) `{(n(n+1))/2}^2` (c) `-{(n(n+1))/2}^2` (d) none of these

Explanation

Correct option is C)
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f(x)=(cos x+i sin x)(cos 2 x+i sin 2 x) `
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(cos 3 x+i sin 3 x) ldots(cos n x+i sin nx) `
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=cos (x+2 x=3 x+ldots+nx)+i sin (x+2 x+3 x+ldots+nx) `
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