Question

Prove that Left hand side = right hand side, pls help ​

Answer 1

$lhs = ( {cot \alpha + cosec \alpha })^{2} \\ = ({ \frac{cos \alpha }{sin \alpha } + \frac{1}{sin \alpha } })^{2} = ({ \frac{ \cos\alpha + 1}{ \sin \alpha } })^{2} \\ = \frac{( {cos \alpha + 1})^{2} }{sin^{2} \alpha } = \frac{ ({cos \alpha + 1})^{2} }{1 - cos^{2} \alpha } \\ \frac{ (1 + cos \alpha )^{2} }{(1 + cos \alpha )(1 - cos \alpha )} = \frac{1 + cos \alpha }{1 - cos \alpha } = rhs$