Trigonometry Examples

$\cos (\frac{π}{2} - x) \csc (- x)$

Step 1

Since $\csc (- x)$ is an odd function, rewrite $\csc (- x)$ as $- \csc (x)$ .

$\cos (\frac{π}{2} - x) (- \csc (x))$

Step 2

Rewrite using the commutative property of multiplication.

$- \cos (\frac{π}{2} - x) \csc (x)$

Step 3

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

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

Step 4

Combine $\frac{1}{\sin (x)}$ and $\cos (\frac{π}{2} - x)$ .

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

Step 5

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

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

Step 6

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

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

Step 7

Simplify.

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Step 7.1

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

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

Step 7.2

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

$- (\cos (\frac{π}{2} - x) \csc (x))$

$- \cos (\frac{π}{2} - x) \csc (x)$