Question

Prove that cos0/1-tan0 +sin0/1-cot0 =sin0 +cos0
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Answer 1

$LHS =\red{ \frac{ cos 0}{1- tan0 } + \frac{ sin 0}{1- cot 0 } }$

$= \frac{ cos^{2} 0}{cos 0(1- tan0) } + \frac{ sin^{2} 0}{sin 0 (1- cot 0) }$

$= \frac{ cos^{2} 0}{(cos 0- sin 0) } + \frac{ sin^{2} 0}{(sin 0 - cos 0) }$

$= \frac{ cos^{2} 0}{(cos 0- sin 0) } - \frac{ sin^{2} 0}{(cos 0 - sin 0) }$

$= \frac{ (cos^{2} 0 - sin^{2} 0)}{(cos 0 - sin 0) }$

$= \frac{ (cos0 - sin 0)( cos 0 + sin 0)}{(cos 0 - sin 0) }$

$\green { = sin 0 + cos 0 } \\= RHS$

$Hence \:proved$

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Answer 2

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