Question

cosec square A - 1/cosec square A= cos square A​

Answer 1

$\frac{ \csc {}^{2} (a) - 1}{ \csc {}^{2} (a) } = \cos {}^{2} (a) \\ \frac{ \frac{1}{ \sin {}^{2} (a) } - 1 }{ \frac{1}{ \sin {}^{2} (a) } } = \cos {}^{2} (a) \\ \frac{ \frac{1 - \sin {}^{2} (a) }{ \sin {}^{2} (a) } }{ \frac{1}{ \sin {}^{2} (a) } } = \cos {}^{2} (a) \\ \frac{ \frac{ \cos {}^{2} (a) }{ \sin {}^{2} (a) } }{ \frac{1}{ \sin {}^{2} (a) } } = \cos {}^{2} (a) \\ \frac{ \cos {}^{2} (a) }{ \sin {}^{2} (a) } \times \frac{ \sin {}^{2} (a) }{ 1} = \cos {}^{2} (a) \ \\ cos {}^{2} (a) = \cos {}^{2} (a) \\ \\ hence \: lhs = rhs$

Hence L.H.S =R.H.S

I hope that helps you...