Question

solve only if you know otherwise will report you (*_*)​

Answer 1

SOLUTION :

$\\ \\ \\ \\ \\ \\ = \frac{cosec \: A\:(cosec \: A + 1) + cosec \: A(cose c\: A - 1)}{ {cosec}^{2}A - 1 } \\ \\ \\ \\ \\ = \frac{ {cosec}^{2} A + {cosec}^{2} A + cosec \: A - cosec \:A }{ {cot}^{2}A } \\ \\ \\ \\ \\ = \frac{2 {cosec}^{2}A }{ {cot}^{2}A } \\ \\ \\ \\ = 2 {sec}^{2} A \\ \\ \\ \\ \\ lhs = rhs(proved)$