Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

$\cos^{2} (θ) + \cos^{2} (θ) + {(\frac{\sin (θ)}{\cos (θ)})}^{2}$

Step 1.2

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

$\cos^{2} (θ) + \cos^{2} (θ) + \frac{\sin^{2} (θ)}{\cos^{2} (θ)}$

Step 2

Add $\cos^{2} (θ)$ and $\cos^{2} (θ)$ .

$2 \cos^{2} (θ) + \frac{\sin^{2} (θ)}{\cos^{2} (θ)}$

Step 3

Convert from $\frac{\sin^{2} (θ)}{\cos^{2} (θ)}$ to $\tan^{2} (θ)$ .

$2 \cos^{2} (θ) + \tan^{2} (θ)$