Precalculus Examples

$\sec^{2} (θ) (1 - \sin^{2} (θ)) = 1$

Step 1

Start on the left side.

$\sec^{2} (θ) (1 - \sin^{2} (θ))$

Step 2

Apply pythagorean identity.

$\sec^{2} (θ) \cos^{2} (θ)$

Step 3

Convert to sines and cosines.

Tap for more steps...

Step 3.1

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

${(\frac{1}{\cos (θ)})}^{2} \cos^{2} (θ)$

Step 3.2

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

$\frac{1^{2}}{\cos^{2} (θ)} \cos^{2} (θ)$

Step 4

Simplify.

Tap for more steps...

Step 4.1

One to any power is one.

$\frac{1}{{\cos (θ)}^{2}} {\cos (θ)}^{2}$

Step 4.2

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

Tap for more steps...

Step 4.2.1

Cancel the common factor.

$\frac{1}{{\cos (θ)}^{2}} {\cos (θ)}^{2}$

Step 4.2.2

Rewrite the expression.

$1$

Step 5

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

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