Verified Answer :

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

Because of this...

\(\frac { 1 }{ 1+\cot ^{ 2 }{ x } } \\ \\ =\frac { 1 }{ \csc ^{ 2 }{ x } }\)

But...

\(\frac { 1 }{ \csc ^{ 2 }{ x } } =\sin ^{ 2 }{ x }\)

Therefore:

\(\frac { 1 }{ 1+\cot ^{ 2 }{ x } } =\sin ^{ 2 }{ x }\)

Answer:

(c)

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