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Question: If \(\frac{1 - \cos x}{\cos x(1 + \cos x)} = \frac{\sin\alpha}{\cos x} - \frac{2}{1 + \cos x}\), the...

If 1−cos⁡xcos⁡x(1+cos⁡x)=sin⁡αcos⁡x−21+cos⁡x\frac{1 - \cos x}{\cos x(1 + \cos x)} = \frac{\sin\alpha}{\cos x} - \frac{2}{1 + \cos x}, then α=\alpha =

A

π/8

B

π/4

C

π/2

D

π\pi

Answer

π/2

Explanation

Solution

1−cos⁡x=sin⁡α(1+cos⁡x)−2cos⁡x1 - \cos x = \sin\alpha(1 + \cos x) - 2\cos x

⇒1=sin⁡α,−1=−2+sin⁡α⇒α=π2\Rightarrow 1 = \sin\alpha, - 1 = - 2 + \sin\alpha \Rightarrow \alpha = \frac{\pi}{2}.