Question

prove the following identity
sinx +cosx sinx - cosx 2
--------------- + ---------------- = -------------
sinx - cosx sinx+ cosx 2sin²x - 1 ​

Answer 1

Answer:

Use the Property : $sin^2x +cos^2x = 1$

$LHS:$ $\frac{sin\:x \: - \:cos\: x }{sin\:x \: + \: cos\: x}$

$= \frac{sin\:x\: -\:cos\:x}{sin\:x\: +\:cos\:x} . \frac{sin\:x\: +\:cos\:x}{sin\:x\: +\:cos\:x} -> \bold{multiply\:by \: conjucate }$

$= \frac{2 sin^2 x -1}{1 + 2\:sin\:x\:cos\:x}$

$\bold{Hence, proved}$

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