Simplify sin(x)^2+tan(x)^2

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

Step 1

Simplify each term.

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

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

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

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

Step 2

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

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