Trigonometry Examples

$\tan (A) \sin (A)$

Step 1

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

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

Step 2

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

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Step 2.1

Combine $\frac{\sin (A)}{\cos (A)}$ and $\sin (A)$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

Add $1$ and $1$ .

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

Step 3

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

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

Step 4

Separate fractions.

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

Step 5

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

$\frac{\sin (A)}{1} \tan (A)$

Step 6

Divide $\sin (A)$ by $1$ .

$\sin (A) \tan (A)$