Expand Using Sum/Difference Formulas tan(90 degrees -theta)

$\tan (90 ° - θ)$

Use the difference formula for tangent to simplify the expression. The formula states that $\tan (A - B) = \frac{\tan (A) - \tan (B)}{1 + \tan (A) \tan (B)}$ .

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

Remove parentheses.

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

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

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

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

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

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

Undefined

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