Trigonometry Examples

$\frac{\sqrt{3 + 5}}{\sqrt{3 - 5}}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Add $3$ and $5$ .

$\frac{\sqrt{8}}{\sqrt{3 - 5}}$

Step 1.2

Rewrite $8$ as $2^{2} \cdot 2$ .

Tap for more steps...

Step 1.2.1

Factor $4$ out of $8$ .

$\frac{\sqrt{4 (2)}}{\sqrt{3 - 5}}$

Step 1.2.2

Rewrite $4$ as $2^{2}$ .

$\frac{\sqrt{2^{2} \cdot 2}}{\sqrt{3 - 5}}$

$\frac{\sqrt{2^{2} \cdot 2}}{\sqrt{3 - 5}}$

Step 1.3

Pull terms out from under the radical.

$\frac{2 \sqrt{2}}{\sqrt{3 - 5}}$

$\frac{2 \sqrt{2}}{\sqrt{3 - 5}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Subtract $5$ from $3$ .

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

Step 2.2

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{2 \sqrt{2}}{\sqrt{- 1 (2)}}$

Step 2.3

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$\frac{2 \sqrt{2}}{\sqrt{- 1} \cdot \sqrt{2}}$

Step 2.4

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{2 \sqrt{2}}{i \sqrt{2}}$

$\frac{2 \sqrt{2}}{i \sqrt{2}}$

Step 3

Cancel the common factor of $\sqrt{2}$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{2 \sqrt{2}}{i \sqrt{2}}$

Step 3.2

Rewrite the expression.

$\frac{2}{i}$

$\frac{2}{i}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$