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Question: If \(\cos\alpha + \cos\beta + \cos\gamma,\) is a positive integer, then which of the following relat...

If cos⁡α+cos⁡β+cos⁡γ,\cos\alpha + \cos\beta + \cos\gamma, is a positive integer, then which of the following relations is false.

A

sin⁡α+sin⁡β+sin⁡γ=0=\sin\alpha + \sin\beta + \sin\gamma = 0 =

B

cos⁡8θ+isin⁡8θ\cos 8\theta + i\sin 8\theta

C

sin⁡8θ+icos⁡8θ\sin 8\theta + i\cos 8\theta

D

cos⁡8θ−isin⁡8θ\cos 8\theta - i\sin 8\theta

Answer

cos⁡8θ+isin⁡8θ\cos 8\theta + i\sin 8\theta

Explanation

Solution

We know that

+∣z1−z2∣2+ |z_{1} - z_{2}|^{2} ⇒ 2∣z1∣2∣z2∣22|z_{1}|^{2}|z_{2}|^{2}

and therefore 2∣z1∣2+2∣z2∣22|z_{1}|^{2} + 2|z_{2}|^{2}