Trigonometry Examples

$\sqrt{1 - \sec^{2} (x)}$

Step 1

Simplify with factoring out.

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Step 1.1

Reorder $1$ and $- \sec^{2} (x)$ .

$\sqrt{- \sec^{2} (x) + 1}$

Step 1.2

Factor $- 1$ out of $- \sec^{2} (x)$ .

$\sqrt{- (\sec^{2} (x)) + 1}$

Step 1.3

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

$\sqrt{- \sec^{2} (x) - 1 \cdot - 1}$

Step 1.4

Factor $- 1$ out of $- \sec^{2} (x) - 1 \cdot - 1$ .

$\sqrt{- (\sec^{2} (x) - 1)}$

$\sqrt{- (\sec^{2} (x) - 1)}$

Step 2

Apply pythagorean identity.

$\sqrt{- \tan^{2} (x)}$

Step 3

Simplify by cancelling exponent with radical.

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Step 3.1

Reorder $- 1$ and $\tan^{2} (x)$ .

$\sqrt{\tan^{2} (x) \cdot - 1}$

Step 3.2

Pull terms out from under the radical.

$\tan (x) \sqrt{- 1}$

$\tan (x) \sqrt{- 1}$

Step 4

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

$\tan (x) i$

Step 5

Reorder factors in $\tan (x) i$ .

$i \tan (x)$

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