Question

Verify that 1 + cot2 x = csc2 x is an identity.

Answer 1

$\sin ^{ 2 }{ x } +\cos ^{ 2 }{ x } =1\\ \\ \frac { \sin ^{ 2 }{ x+\cos ^{ 2 }{ x } } }{ \sin ^{ 2 }{ x } } =\frac { 1 }{ \sin ^{ 2 }{ x } }$

$\\ \\ \frac { \sin ^{ 2 }{ x } }{ \sin ^{ 2 }{ x } } +\frac { \cos ^{ 2 }{ x } }{ \sin ^{ 2 }{ x } } =\frac { 1 }{ \sin ^{ 2 }{ x } } \\ \\ 1+\cot ^{ 2 }{ x } =\csc ^{ 2 }{ x }$