Precalculus Examples

$\cos (x) + \sin^{2} (x) \sec (x)$

Step 1

Simplify each term.

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Step 1.1

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

$\cos (x) + \sin^{2} (x) \frac{1}{\cos (x)}$

Step 1.2

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

$\cos (x) + \frac{\sin^{2} (x)}{\cos (x)}$

Step 2

Simplify each term.

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Step 2.1

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

$\cos (x) + \frac{\sin (x) \sin (x)}{\cos (x)}$

Step 2.2

Separate fractions.

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

Step 2.3

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$\cos (x) + \frac{\sin (x)}{1} \tan (x)$

Step 2.4

Divide $\sin (x)$ by $1$ .

$\cos (x) + \sin (x) \tan (x)$