Trigonometry Examples

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

Step 1

Factor $\sin (\frac{π}{2} - x)$ out of $\sin^{2} (\frac{π}{2} - x)$ .

$\frac{\sin (\frac{π}{2} - x) \sin (\frac{π}{2} - x)}{\sin (x)}$

Step 2

Separate fractions.

$\frac{\sin (\frac{π}{2} - x)}{1} \cdot \frac{\sin (\frac{π}{2} - x)}{\sin (x)}$

Step 3

Rewrite $\frac{\sin (\frac{π}{2} - x)}{\sin (x)}$ as a product.

$\frac{\sin (\frac{π}{2} - x)}{1} (\sin (\frac{π}{2} - x) \frac{1}{\sin (x)})$

Step 4

Write $\sin (\frac{π}{2} - x)$ as a fraction with denominator $1$ .

$\frac{\sin (\frac{π}{2} - x)}{1} (\frac{\sin (\frac{π}{2} - x)}{1} \cdot \frac{1}{\sin (x)})$

Step 5

Simplify.

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Step 5.1

Divide $\sin (\frac{π}{2} - x)$ by $1$ .

$\frac{\sin (\frac{π}{2} - x)}{1} (\sin (\frac{π}{2} - x) \frac{1}{\sin (x)})$

Step 5.2

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

$\frac{\sin (\frac{π}{2} - x)}{1} (\sin (\frac{π}{2} - x) \csc (x))$

Step 6

Divide $\sin (\frac{π}{2} - x)$ by $1$ .

$\sin (\frac{π}{2} - x) (\sin (\frac{π}{2} - x) \csc (x))$

Step 7

Multiply $\sin (\frac{π}{2} - x) (\sin (\frac{π}{2} - x) \csc (x))$ .

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Step 7.1

Raise $\sin (\frac{π}{2} - x)$ to the power of $1$ .

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

Step 7.2

Raise $\sin (\frac{π}{2} - x)$ to the power of $1$ .

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

Step 7.3

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

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

Step 7.4

Add $1$ and $1$ .

$\sin^{2} (\frac{π}{2} - x) \csc (x)$