Trigonometry Examples

$\cot (\frac{π}{2} - x) \cos (x)$

Step 1

Apply the difference of angles identity.

$\frac{\cot (\frac{π}{2}) \cot (x) + 1}{\cot (x) - \cot (\frac{π}{2})} \cos (x)$

Step 2

Simplify the numerator.

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Step 2.1

The exact value of $\cot (\frac{π}{2})$ is $0$ .

$\frac{0 \cot (x) + 1}{\cot (x) - \cot (\frac{π}{2})} \cos (x)$

Step 2.2

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

$\frac{0 \frac{\cos (x)}{\sin (x)} + 1}{\cot (x) - \cot (\frac{π}{2})} \cos (x)$

Step 2.3

Multiply $0$ by $\frac{\cos (x)}{\sin (x)}$ .

$\frac{0 + 1}{\cot (x) - \cot (\frac{π}{2})} \cos (x)$

Step 2.4

Add $0$ and $1$ .

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

The exact value of $\cot (\frac{π}{2})$ is $0$ .

$\frac{1}{\frac{\cos (x)}{\sin (x)} - 0} \cos (x)$

Step 3.3

Multiply $- 1$ by $0$ .

$\frac{1}{\frac{\cos (x)}{\sin (x)} + 0} \cos (x)$

Step 3.4

Add $\frac{\cos (x)}{\sin (x)}$ and $0$ .

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

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

Step 5

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

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

Step 6

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

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\sin (x)$