Question

Prove that cot-cos/cot+cos=cosec-1/cosec+1

Answer 1

I hope this helps you.

Answer 2

$LHS = \frac{cot A - cosA }{cot A + cos A} \\= \frac{\frac{cos A}{sin A} - cos A}{\frac{cosA}{sinA} - cosA} \\= \frac{cosA\Big(\frac{1}{sin A} - 1\Big)}{cosA\Big(\frac{1}{sinA} - 1\Big)} \\= \frac{\Big(\frac{1}{sin A} - 1\Big)}{\Big(\frac{1}{sinA} - 1\Big)} \\= \frac{ (Cosec A - 1 )}{(Cosec A + 1)}$

$\boxed { \pink { Since , \frac{1}{sin A} = Cosec A }}$

$= RHS$

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