Question

prove that
tanA+cot2A=cosec2A

Answer 1

taking LHS

tanA+cot2a

$\frac{ \sin(a) }{ \cos(a) } + \frac{ \cos(2a) }{ \sin(2a) } \\ \frac{ \sin(a) }{ \cos(a) } + \frac{ \cos(2a) }{2 \sin(a) \cos(a) } \\ \frac{ { 2\sin }^{2}a + { \cos}^{2} a - { \sin }^{2}a }{2 \sin(a) \cos(a) } \\ \frac{ {sin}^{2} a + {cos}^{2}a }{2 \sin(a) \cos(a) } \\ \frac{1}{2 \sin(a) \cos(a) } \\ \frac{1}{ \sin(2a) } \\ cosec2a = r.h.s$

hope it will help you!!