Precalculus Examples

$\cot (90 ° - θ)$

Step 1

Apply the difference of angles identity.

$\frac{\cot (90 °) \cot (θ) + 1}{\cot (θ) - \cot (90 °)}$

Step 2

Simplify the numerator.

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Step 2.1

The exact value of $\cot (90 °)$ is $0$ .

$\frac{0 \cot (θ) + 1}{\cot (θ) - \cot (90 °)}$

Step 2.2

Multiply $0$ by $\cot (θ)$ .

$\frac{0 + 1}{\cot (θ) - \cot (90 °)}$

Step 2.3

Add $0$ and $1$ .

$\frac{1}{\cot (θ) - \cot (90 °)}$

Step 3

Simplify the denominator.

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Step 3.1

The exact value of $\cot (90 °)$ is $0$ .

$\frac{1}{\cot (θ) - 0}$

Step 3.2

Multiply $- 1$ by $0$ .

$\frac{1}{\cot (θ) + 0}$

Step 3.3

Add $\cot (θ)$ and $0$ .

$\frac{1}{\cot (θ)}$

Step 4

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

$\frac{1}{\frac{\cos (θ)}{\sin (θ)}}$

Step 5

Multiply by the reciprocal of the fraction to divide by $\frac{\cos (θ)}{\sin (θ)}$ .

$\frac{\sin (θ)}{\cos (θ)}$

Step 6

Convert from $\frac{\sin (θ)}{\cos (θ)}$ to $\tan (θ)$ .

$\tan (θ)$