Trigonometry Examples

$\cos (t) (1 + \tan^{2} (t))$

Step 1

Rearrange terms.

$\cos (t) (\tan^{2} (t) + 1)$

Step 2

Apply pythagorean identity.

$\cos (t) \sec^{2} (t)$

Step 3

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

$\cos (t) {(\frac{1}{\cos (t)})}^{2}$

Step 4

Simplify the expression.

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Step 4.1

Apply the product rule to $\frac{1}{\cos (t)}$ .

$\cos (t) \frac{1^{2}}{\cos^{2} (t)}$

Step 4.2

One to any power is one.

$\cos (t) \frac{1}{\cos^{2} (t)}$

$\cos (t) \frac{1}{\cos^{2} (t)}$

Step 5

Cancel the common factor of $\cos (t)$ .

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Step 5.1

Factor $\cos (t)$ out of $\cos^{2} (t)$ .

$\cos (t) \frac{1}{\cos (t) \cos (t)}$

Step 5.2

Cancel the common factor.

$\cos (t) \frac{1}{\cos (t) \cos (t)}$

Step 5.3

Rewrite the expression.

$\frac{1}{\cos (t)}$

$\frac{1}{\cos (t)}$

Step 6

Convert from $\frac{1}{\cos (t)}$ to $\sec (t)$ .

$\sec (t)$

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