Trigonometry Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

Divide $\frac{1}{\sin (x)}$ by $1$ .

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

Step 4

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

$\csc (x) \csc (x)$

Step 5

Multiply $\csc (x) \csc (x)$ .

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Step 5.1

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

$\csc^{1} (x) \csc (x)$

Step 5.2

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

$\csc^{1} (x) \csc^{1} (x)$

Step 5.3

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

${\csc (x)}^{1 + 1}$

Step 5.4

Add $1$ and $1$ .

$\csc^{2} (x)$