Algebra Examples

Simplify $\cos^{2} (θ) + \cos^{2} (θ) \cdot \tan^{2} (θ)$

Step 1

Multiply by $1$ .

$\cos^{2} (θ) \cdot 1 + \cos^{2} (θ) \cdot \tan^{2} (θ)$

Step 2

Factor $\cos^{2} (θ)$ out of $\cos^{2} (θ) \cdot \tan^{2} (θ)$ .

$\cos^{2} (θ) \cdot 1 + \cos^{2} (θ) (\tan^{2} (θ))$

Step 3

Factor $\cos^{2} (θ)$ out of $\cos^{2} (θ) \cdot 1 + \cos^{2} (θ) (\tan^{2} (θ))$ .

$\cos^{2} (θ) \cdot (1 + \tan^{2} (θ))$

Step 4

Rearrange terms.

$\cos^{2} (θ) \cdot (\tan^{2} (θ) + 1)$

Step 5

Apply pythagorean identity.

$\cos^{2} (θ) \cdot \sec^{2} (θ)$

Step 6

Rewrite $\sec (θ)$ in terms of sines and cosines.

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

Step 7

Simplify the expression.

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Step 7.1

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

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

Step 7.2

One to any power is one.

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

Step 8

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

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Step 8.1

Cancel the common factor.

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

Step 8.2

Rewrite the expression.

$1$