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Circular Measurement of Angle

Prove that c...

Question

Prove that
$\frac{c o s A}{1 - t a n A} + \frac{s i n A}{1 - c o t A} = s i n A + c o s A$

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Solution

$L H S =$ $\frac{C o s A}{1 - T a n A} + \frac{S i n A}{1 - C o t A} = \frac{C o s A}{1 - \frac{S i n A}{C o s A}} + \frac{S i n A}{1 - \frac{C o s A}{S i n A}} = \frac{C o s^{2} A - S i n^{2} A}{C o s A - S i n A} = C o s A + S i n A$ $= R H S$

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