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The complex numbers $\sin x + i \cos 2 x$ and $\cos x - i \sin 2 x$ are conjugate to each other for

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x=nπ,n∈I

x=n+12π,n∈I

x=0

no value of x.

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detailed solution

Correct option is D

sin⁡x+icos⁡2x¯=cos⁡x−isin⁡2x⇒ sin⁡x−icos⁡2x=cos⁡x−isin⁡2x⇒ sin⁡x=cos⁡x and cos⁡2x=sin⁡2x⇒ tan⁡x=1 and tan⁡2x=1These two equations cannot hold simultaneously.

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The complex numbers sin⁡x+icos⁡2x and cos⁡x−isin⁡2x are conjugate to each other for

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The complex numbers $\sin x + i \cos 2 x$ and $\cos x - i \sin 2 x$ are conjugate to each other for