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Question

Question: \(\frac{\sin\theta}{1 - \cot\theta} + \frac{\cos\theta}{1 - \tan\theta}\) equals to...

sin⁡θ1−cot⁡θ+cos⁡θ1−tan⁡θ\frac{\sin\theta}{1 - \cot\theta} + \frac{\cos\theta}{1 - \tan\theta} equals to

A

0

B

1

C

sin⁡15o\sin 15^{o}

D

cos⁡15o\cos 15^{o}

Answer

cos⁡15o\cos 15^{o}

Explanation

Solution

sin⁡15o.cos⁡15o\sin 15^{o}.\cos 15^{o}=sin⁡2θ(sin⁡θ−cos⁡θ)+cos⁡2θ(cos⁡θ−sin⁡θ)\frac{\sin^{2}\theta}{(\sin\theta - \cos\theta)} + \frac{\cos^{2}\theta}{(\cos\theta - \sin\theta)}

= sin⁡15o\sin 15^{o}