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Verify the identity cot x/ csc^2 x= cos x sin x

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(\cot x)/(\csc ^2x)=\text{ cosx sinx}

We will take the left hand side and prove that it is equal to the right -hand side

But, First, we need to note that; cotx = cosx / sinx and csc²x = 1/ sin²x

substitute the values into the the left-hand side of the original equation


((\cos x)/(\sin x))/((1)/(\sin ^2x))


(\cos x)/(\sin x)*(\sin ^2x)/(1)

One of the sinx at the numerator will cancel-out the one at the denominator


=\text{ cosx sinx}

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