Question

1 + cot2A/1+cosecA=cosecA

Answer 1

$to \: prove \\ \: \: \: \: \: \: \: \: \: \: \: \: \frac{1 + {cot \: a}^{2} }{1 + cosec \: a} = {tan}^{3}$

$proving \\ \\ = > \frac{1 + {cos}^{2} a}{1 + cosec \: a} = cosec \: a \\ \\ taking \: l.h.s. \\ = > \frac{ {tan}^{2}a }{1 + \frac{1}{sin \: a} } \\ \\ = > \frac{ \frac{ {sin}^{2}a }{ {cos}^{2}a } }{ \frac{sin \: a + 1}{sin \: a} } \\ \\ = > \frac{ {sin}^{2} a}{ {cos}^{2} a} \times \frac{sin \: a}{1 + sin \: a} \\ \\ = > \frac{sin \: a}{cos \: a} \times \frac{ sin \: a}{1 - sin \: a} \times \frac{sin \: a}{1 + sin \: a} \\ \\ = > \frac{sin \: a}{cos \: a} \times \frac{ {sin}^{2}a }{1 - {sin }^{2}a } \\ \\ = > \frac{sin \: a}{cos \: a} \times \frac{ {sin}^{2} a}{ {cos}^{2}a } \\ \\ = > \frac{ {sin}^{3}a }{ {cos}^{3} a} \\ \\ = > {tan}^{3} a$

$hope \: you \: got \: it$