Trigonometry Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

Add $1$ and $1$ .

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

Step 3

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

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

Step 4

Combine fractions.

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Step 4.1

Combine.

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

Step 4.2

Multiply $\sin^{2} (x)$ by $1$ .

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

Step 5

Simplify the denominator.

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

Add $1$ and $1$ .

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

Step 6

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

$\tan^{2} (x)$