Simplify Simplify cos(theta)+sin(theta)*tan(theta)

Simplify $\cos (θ) + \sin (θ) \cdot \tan (θ)$

Step 1

Simplify each term.

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

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

Multiply $\sin (θ) \frac{\sin (θ)}{\cos (θ)}$ .

Raise $\sin (θ)$ to the power of $1$ .

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

Raise $\sin (θ)$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Step 2

Simplify each term.

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

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

Separate fractions.

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

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

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

Divide $\sin (θ)$ by $1$ .

$\cos (θ) + \sin (θ) \tan (θ)$