Trigonometry Examples

$\cos^{2} (θ) (\tan^{2} (θ) + 1) = 1$

Step 1

Start on the left side.

$\cos^{2} (θ) (\tan^{2} (θ) + 1)$

Step 2

Apply pythagorean identity.

$\cos^{2} (θ) \sec^{2} (θ)$

Step 3

Convert to sines and cosines.

Tap for more steps...

Step 3.1

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

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

Step 3.2

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

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

One to any power is one.

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

Step 4.2

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

Tap for more steps...

Step 4.2.1

Cancel the common factor.

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

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.

$\cos^{2} (θ) (\tan^{2} (θ) + 1) = 1$ is an identity