[tex]\sin ^{ 2 }{ x } +\cos ^{ 2 }{ x } =1\\ \\ \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 } [/tex]
Because of this...
[tex]\frac { 1 }{ 1+\cot ^{ 2 }{ x } } \\ \\ =\frac { 1 }{ \csc ^{ 2 }{ x } } [/tex]
But...
[tex]\frac { 1 }{ \csc ^{ 2 }{ x } } =\sin ^{ 2 }{ x } [/tex]
Therefore:
[tex]\frac { 1 }{ 1+\cot ^{ 2 }{ x } } =\sin ^{ 2 }{ x } [/tex]
Answer:
(c)
