Trigonometry Examples

$\frac{\sec^{2} (x) - 1}{\sec (x)}$

Step 1

Set the denominator in $\frac{\sec^{2} (x) - 1}{\sec (x)}$ equal to $0$ to find where the expression is undefined.

$\sec (x) = 0$

Step 2

The range of secant is $y \leq - 1$ and $y \geq 1$ . Since $0$ does not fall in this range, there is no solution.

No solution

Step 3

Set the argument in $\sec (x)$ equal to $\frac{π}{2} + π n$ to find where the expression is undefined.

$x = \frac{π}{2} + π n$ , for any integer $n$

Step 4

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

${x | x = \frac{π}{2} + π n}$ $n$ , for any integer $n$

Step 5