## Related questions with answers

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

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2Fundamental trigonometric identity:

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

So we have:

$\begin{align*} \dfrac{1}{\cot^2x+1}&=[(1)]=\dfrac{1}{\csc^2x}\Big/ \text{use: } \csc x=\dfrac{1}{\sin x}\\\\ &=\dfrac{1}{\dfrac{1}{\sin^2 x}}\\\\ &=\sin^2x \end{align*}$

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