Trigonometry Examples

$\sqrt{{(9 \tan (x))}^{2} + 81}$

Step 1

Simplify with factoring out.

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Step 1.1

Apply the product rule to $9 \tan (x)$ .

$\sqrt{9^{2} \tan^{2} (x) + 81}$

Step 1.2

Raise $9$ to the power of $2$ .

$\sqrt{81 \tan^{2} (x) + 81}$

Step 1.3

Factor $81$ out of $81 \tan^{2} (x) + 81$ .

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Step 1.3.1

Factor $81$ out of $81 \tan^{2} (x)$ .

$\sqrt{81 (\tan^{2} (x)) + 81}$

Step 1.3.2

Factor $81$ out of $81$ .

$\sqrt{81 (\tan^{2} (x)) + 81 (1)}$

Step 1.3.3

Factor $81$ out of $81 (\tan^{2} (x)) + 81 (1)$ .

$\sqrt{81 (\tan^{2} (x) + 1)}$

Step 2

Apply pythagorean identity.

$\sqrt{81 \sec^{2} (x)}$

Step 3

Rewrite $81 \sec^{2} (x)$ as ${(9 \sec (x))}^{2}$ .

$\sqrt{{(9 \sec (x))}^{2}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$9 \sec (x)$