Question

Prove that 1+sin A -cosA/1+sinA+cosA = √1-cosA/1+cosA​

Answer 1

Answer:

May it will help you

Answer 2

LHS

$\frac{1 + sina - cosa}{1 + sina + cosa} \\ \\ = \frac{ \frac{1 + sina - cosa}{sina} }{ \frac{1 + sina + cosa}{sina} } \\ \\ = \frac{coseca - cota + 1}{coseca + cota + 1} \\ \\ = \frac{(coseca - cota) + ( {cosec}^{2}a - {cot}^{2} a)}{coseca + cota + 1} \\ \\ = \frac{(coseca - cota)(1 + coseca + cota)}{(1 + coseca + cota)} \\ \\ = coseca - cota$

RHS

$\sqrt{ \frac{1 - cosa}{1 + cosa} } \\ \\ = \sqrt{ \frac{1 - cosa}{1 + cosa} \times \frac{1 - cosa}{1 - cosa} } \\ \\ = \sqrt{ \frac{( {1 - cosa})^{2} }{1 - {cos}^{2} a} } \\ \\ = \sqrt{ \frac{( {1 - cosa})^{2} }{ {sin}^{2} a} } \\ \\ = \frac{1 - cosa}{sina} \\ \\ = coseca - cota$

$\therefore \: LHS = RHS$