First slide

Trigonometric equations

Question

$2 \cos^{2} â¡ x + 4 \cos â¡ x = 3 \sin^{2} â¡ x$ if

Moderate

A

$\cos â¡ x = \frac{â 2 + \sqrt{14}}{5}$
B

$\cos â¡ x = \frac{â 2 + \sqrt{19}}{5}$
C

$\sin â¡ x = \frac{â 2 + \sqrt{14}}{5}$
D

$\sin â¡ x = \frac{â 2 + \sqrt{19}}{5}$

Solution

$\begin{array}{l} 2 \cos^{2} â¡ x + 4 \cos â¡ x = 3 (1 â \cos^{2} â¡ x) \\ â 5 \cos^{2} â¡ x + 4 \cos â¡ x â 3 = 0 \\ â \cos â¡ x = \frac{â 4 Â\pm \sqrt{16 + 60}}{10} = \frac{â 2 Â\pm \sqrt{19}}{5} \end{array}$
But $\cos â¡ x â \frac{â 2 â \sqrt{19}}{5}$

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