Precalculus Examples

$\tan (90 ° - θ)$

Step 1

Apply the difference of angles identity.

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

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $\tan (90 °)$ in terms of sines and cosines.

$\frac{\frac{\sin (90 °)}{\cos (90 °)} - \tan (θ)}{1 + \tan (90 °) \tan (θ)}$

Step 2.2

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

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

Step 2.3

The expression contains a division by $0$ . The expression is undefined.

Undefined

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

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $\tan (90 °)$ in terms of sines and cosines.

$\frac{\frac{\sin (90 °)}{0} - \tan (θ)}{1 + \frac{\sin (90 °)}{\cos (90 °)} \tan (θ)}$

Step 3.2

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

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

Step 3.3

The expression contains a division by $0$ . The expression is undefined.

Undefined

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

Step 4

The expression contains a division by $0$ . The expression is undefined.

Undefined