Trigonometry Examples

$\tan (x + \frac{π}{2})$

Step 1

Apply the sum of angles identity.

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

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $\tan (\frac{π}{2})$ in terms of sines and cosines.

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

Step 2.2

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

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

Step 2.3

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

Undefined

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

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $\tan (\frac{π}{2})$ in terms of sines and cosines.

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

Step 3.2

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

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

Step 3.3

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

Undefined

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

Step 4

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

Undefined