Trigonometry Examples

$\sin (\frac{π}{2} - x) \sec (x)$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Simplify.

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Step 5.1

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

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

Step 5.2

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\sin (\frac{π}{2} - x) \sec (x)$