Algebra Examples

\cos (\frac{π}{2} - x) \sec (x)

$\cos (\frac{π}{2} - x) \sec (x)$

Step 1

Rewrite

\sec (x)

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

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

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

Step 2

Combine

\cos (\frac{π}{2} - x)

$\cos (\frac{π}{2} - x)$ and

\frac{1}{\cos (x)}

$\frac{1}{\cos (x)}$ .

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

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

Step 3

Rewrite

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

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

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

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

Step 4

Write

\cos (\frac{π}{2} - x)

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

1

$1$ .

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

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

Step 5

Simplify.

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Step 5.1

Divide

\cos (\frac{π}{2} - x)

$\cos (\frac{π}{2} - x)$ by

1

$1$ .

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

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

Step 5.2

Convert from

\frac{1}{\cos (x)}

$\frac{1}{\cos (x)}$ to

\sec (x)

$\sec (x)$ .

\cos (\frac{π}{2} - x) \sec (x)

$\cos (\frac{π}{2} - x) \sec (x)$

\cos (\frac{π}{2} - x) \sec (x)

$\cos (\frac{π}{2} - x) \sec (x)$