Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Multiply $\frac{1}{\sin (x)} \cdot \frac{\cos (x)}{\sin (x)}$ .

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Step 3.1

Multiply $\frac{1}{\sin (x)}$ by $\frac{\cos (x)}{\sin (x)}$ .

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

Step 3.2

Raise $\sin (x)$ to the power of $1$ .

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

Step 3.3

Raise $\sin (x)$ to the power of $1$ .

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

Step 3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.5

Add $1$ and $1$ .

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

Step 4

Apply pythagorean identity.

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\cos (x)$