Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

One to any power is one.

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

Step 1.4

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

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

Step 2

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

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

Step 3

Rearrange terms.

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

Step 4

Apply pythagorean identity.

$\sec^{2} (x)$