Trigonometry Examples

$\frac{\tan (\frac{π}{3})}{2} - \frac{1}{\sec (\frac{π}{6})}$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\tan (\frac{π}{3})$ is $\sqrt{3}$ .

$\frac{\sqrt{3}}{2} - \frac{1}{\sec (\frac{π}{6})}$

Step 1.2

Rewrite $\sec (\frac{π}{6})$ in terms of sines and cosines.

$\frac{\sqrt{3}}{2} - \frac{1}{\frac{1}{\cos (\frac{π}{6})}}$

Step 1.3

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (\frac{π}{6})}$ .

$\frac{\sqrt{3}}{2} - (1 \cos (\frac{π}{6}))$

Step 1.4

Multiply $\cos (\frac{π}{6})$ by $1$ .

$\frac{\sqrt{3}}{2} - \cos (\frac{π}{6})$

Step 1.5

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{\sqrt{3} - \sqrt{3}}{2}$

Step 2.2

Subtract $\sqrt{3}$ from $\sqrt{3}$ .

$\frac{0}{2}$

Step 2.3

Divide $0$ by $2$ .

$0$