Question

prove that cot2/1+cosec =1/sin​

Answer 1

$1 + \frac{{ \cot }^{2}x }{1 + cosec \: x } \\ = 1 + \frac{ {cosec}^{2} \: x - 1 }{1 + cosec \: x \: } \\ = 1 + \frac{ (cosec \: x - 1)( cosec \: x + 1 \: )}{(1 + cosec \: x) } \\ = 1 + cosec \: x \: - 1 \\ = cosec \: x \\ = \frac{1}{sin \: x}$

hence prove