Verified Answer :

konrad509

\(\dfrac{\cot x}{1+\csc x}=\dfrac{\csc x-1}{\cot x}\\ \cot^2 x=(1+\csc x)(\csc x-1)\\ \cot^2 x=-(1+\csc x)(1-\csc x)\\ \cot^2 x=-(1-\csc^2 x)\\ \cot^2 x=-1+\csc^2 x\\ \left(\dfrac{\cos x}{\sin x}\right)^2=-1+\left(\dfrac{1}{\sin x}\right)^2\\ \dfrac{\cos^2 x}{\sin ^2x}=-1+\dfrac{1}{\sin^2 x}\\ \cos^2 x=-\sin^2x +1\\ \boxed{\sin^2 x+\cos ^2 x=1}\)

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