Simplify sin(theta)^2+sin(theta)^2*tan(theta)^2

$\sin^{2} (θ) + \sin^{2} (θ) \cdot \tan^{2} (θ)$

Step 1

Multiply by $1$ .

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

Step 2

Factor $\sin^{2} (θ)$ out of $\sin^{2} (θ) \cdot \tan^{2} (θ)$ .

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

Step 3

Factor $\sin^{2} (θ)$ out of $\sin^{2} (θ) \cdot 1 + \sin^{2} (θ) (\tan^{2} (θ))$ .

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

Step 4

Rearrange terms.

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

Step 5

Apply pythagorean identity.

$\sin^{2} (θ) \cdot \sec^{2} (θ)$

Step 6

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

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

Step 7

Simplify the expression.

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

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

One to any power is one.

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

Step 8

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

$\frac{\sin^{2} (θ)}{\cos^{2} (θ)}$

Step 9

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

$\tan^{2} (θ)$