Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

One to any power is one.

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

Step 2

Simplify each term.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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