Simplify tan(theta)sec(theta)sin(theta)

$\tan (θ) \sec (θ) \sin (θ)$

Step 1

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

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

Step 2

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

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

Step 3

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

Multiply $\frac{\sin (θ)}{\cos (θ)}$ by $\frac{1}{\cos (θ)}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Step 4

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

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

$\frac{\sin^{2} (θ)}{\cos^{2} (θ)}$

Step 5

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

$\tan^{2} (θ)$