First slide

Trigonometric equations

Question

$6 \tan^{2} â¡ x â 2 \cos^{2} â¡ x = \cos â¡ 2 x$ if

Moderate

A

$\cos â¡ 2 x = â 1$
B

$\cos â¡ 2 x = 1$
C

$\cos â¡ 3 x = â 1 / 2$
D

$\cos â¡ 2 x = 1 / 2$

Solution

$\begin{array}{l} 6 \sin^{2} â¡ x â 2 \cos^{4} â¡ x = \cos^{2} â¡ x (2 \cos^{2} â¡ x â 1) \\ â 4 \cos^{4} â¡ x + 5 \cos^{2} â¡ x â 6 = 0 \\ â \cos^{2} â¡ x = 3 / 4 = \cos â¡ 2 x = 1 / 2 \end{array}$

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