Question

(1 - cos O) cosec2 theta= 1
Prove this identity​

Answer 1

$(1 - \cos {}^{2} \alpha ) \csc {}^{2} \alpha \\ \\ = \csc {}^{2} \alpha - \frac{ \cos {}^{2} \alpha }{ \sin {}^{2} \alpha } \\ \\ = \csc {}^{2} \alpha - \cot {}^{2} \alpha = 1 = rhs \: \\ \\ hence \: proved \\ \\( ( \frac{ \cos \alpha }{ \sin \alpha } ) = \cot\alpha )$