Trigonometry Examples

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

Step 1

Start on the left side.

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

Step 2

Apply pythagorean identity.

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

Step 3

Convert to sines and cosines.

Tap for more steps...

Step 3.1

Apply the reciprocal identity to $\sec (x)$ .

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

Step 3.2

Apply the product rule to $\frac{1}{\cos (x)}$ .

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify each term.

Tap for more steps...

Step 4.1.1

One to any power is one.

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

Step 4.1.2

Cancel the common factor of ${\cos (x)}^{2}$ .

Tap for more steps...

Step 4.1.2.1

Cancel the common factor.

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

Step 4.1.2.2

Rewrite the expression.

$1 - 1$

Step 4.2

Subtract $1$ from $1$ .

$0$

Step 5

Because the two sides have been shown to be equivalent, the equation is an identity.

$\sec^{2} (x) (1 - \sin^{2} (x)) - 1 = 0$ is an identity