Trigonometry Examples

$\sin (x) \sec (x) \tan (x)$

Step 1

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

$\sin (x) \frac{1}{\cos (x)} \tan (x)$

Step 2

Combine $\sin (x)$ and $\frac{1}{\cos (x)}$ .

$\frac{\sin (x)}{\cos (x)} \tan (x)$

Step 3

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

$\frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)}$

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

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

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

Step 4.5

Add $1$ and $1$ .

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

Step 4.6

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

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

Step 4.7

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

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

Step 4.8

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

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

Step 4.9

Add $1$ and $1$ .

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

Step 5

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

$\tan^{2} (x)$