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Question

use the fundamental trigonometric identities to simplify the expression. There is more than one correct form of each answer. 1 / cot^2 x + 1

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Answered 2 years ago
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Fundamental trigonometric identity:

1+cot2x=csc2x,  (1)\boxed{1+\cot^2x=\csc^2x,~~(1)}

So we have:

1cot2x+1=[(1)]=1csc2x/use: cscx=1sinx=11sin2x=sin2x\begin{align*} \dfrac{1}{\cot^2x+1}&=[(1)]=\dfrac{1}{\csc^2x}\Big/ \text{use: } \csc x=\dfrac{1}{\sin x}\\\\ &=\dfrac{1}{\dfrac{1}{\sin^2 x}}\\\\ &=\sin^2x \end{align*}

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