# Solve for the following equation in the interval [0, 2pi): 3cos^2theta + sin^2theta =2?

## Solve for the following equation in the interval [0, 2$\pi$): $3 {\cos}^{2} \theta + {\sin}^{2} \theta = 2$?

Dec 16, 2017

$\theta = \frac{\pi}{4} , \frac{3 \pi}{4} , \frac{5 \pi}{4} , \frac{7 \pi}{4}$

#### Explanation:

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$3 {\cos}^{2} \theta + {\sin}^{2} \theta = 2$

$3 {\cos}^{2} \theta + 1 - {\cos}^{2} \theta = 2$

$2 {\cos}^{2} \theta = 1$

${\cos}^{2} \theta = \frac{1}{2}$

$\cos \theta = \pm \frac{\sqrt{2}}{2}$

$\theta = \frac{\pi}{4} , \frac{3 \pi}{4} , \frac{5 \pi}{4} , \frac{7 \pi}{4}$