Trigonometry Examples

$\sin^{- 2} (x) \sin (x)$

Step 1

Multiply $\sin^{- 2} (x)$ by $\sin (x)$ by adding the exponents.

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Step 1.1

Multiply $\sin^{- 2} (x)$ by $\sin (x)$ .

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Step 1.1.1

Raise $\sin (x)$ to the power of $1$ .

$\sin^{- 2} (x) \sin^{1} (x)$

Step 1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.2

Add $- 2$ and $1$ .

$\sin^{- 1} (x)$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{\sin (x)}$

Step 3

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

$\csc (x)$