Trigonometry Examples

$\sin (x) (1 + \cot^{2} (x))$

Step 1

Apply pythagorean identity.

$\sin (x) \csc^{2} (x)$

Step 2

Rewrite $\csc (x)$ in terms of sines and cosines.

$\sin (x) {(\frac{1}{\sin (x)})}^{2}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{1}{\sin (x)}$ .

$\sin (x) \frac{1^{2}}{\sin^{2} (x)}$

Step 3.2

One to any power is one.

$\sin (x) \frac{1}{\sin^{2} (x)}$

$\sin (x) \frac{1}{\sin^{2} (x)}$

Step 4

Cancel the common factor of $\sin (x)$ .

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Step 4.1

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

$\sin (x) \frac{1}{\sin (x) \sin (x)}$

Step 4.2

Cancel the common factor.

$\sin (x) \frac{1}{\sin (x) \sin (x)}$

Step 4.3

Rewrite the expression.

$\frac{1}{\sin (x)}$

$\frac{1}{\sin (x)}$

Step 5

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\csc (x)$

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