Trigonometry Examples

$\frac{\sec^{2} (x) - (\tan^{2} (x))}{\cos^{2} (x) + \sin^{2} (x)}$

Step 1

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

$\cos^{2} (x) + \sin^{2} (x) = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Replace the $\cos^{2} (x)$ with $1 - \sin^{2} (x)$ based on the $\sin^{2} (x) + \cos^{2} (x) = 1$ identity.

$(1 - \sin^{2} (x)) + \sin^{2} (x) = 0$

Step 2.2

Combine the opposite terms in $1 - \sin^{2} (x) + \sin^{2} (x)$ .

Tap for more steps...

Step 2.2.1

Add $- \sin^{2} (x)$ and $\sin^{2} (x)$ .

$1 + 0 = 0$

Step 2.2.2

Add $1$ and $0$ .

$1 = 0$

Step 2.3

The equation is never true.

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