Precalculus Examples

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

Step 1

Rearrange terms.

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

Step 2

Apply pythagorean identity.

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

Step 3

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

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

Step 4

Simplify the expression.

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Step 4.1

Apply the product rule to $\frac{1}{\cos (x)}$ .

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

Step 4.2

One to any power is one.

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

Step 5

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

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

Step 6

Convert from $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ to $\tan^{2} (x)$ .

$\tan^{2} (x)$