Simplify sin(x)^2+csc(x)^2

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Algebra

$\sin^{2} (x) + \csc^{2} (x)$

Simplify each term.

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Rewrite $\csc (x)$ in terms of sines and cosines.

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

Apply the product rule to $\frac{1}{\sin (x)}$ .

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

One to any power is one.

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

Simplify each term.

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Rewrite $1$ as $1^{2}$ .

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

Rewrite $\frac{1^{2}}{\sin^{2} (x)}$ as ${(\frac{1}{\sin (x)})}^{2}$ .

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

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\sin^{2} (x) + \csc^{2} (x)$

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