Trigonometry Examples

$\csc^{2} (x) (1 - \cos^{2} (x))$

Step 1

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

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

Step 2

Simplify the expression.

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Step 2.1

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

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

Step 2.2

One to any power is one.

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

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

Step 3

Apply pythagorean identity.

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

Step 4

Cancel the common factor of $\sin^{2} (x)$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$1$

$1$

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