First slide

Trigonometric equations

Question

Number of solutions of the equation $\cos^{4} 2 x + 2 \sin^{2} 2 x = 17 (\cos x + \sin x)^{8}, 0 < x < 2 π$ is

Moderate

A
B
C
D

Solution

Let $\sin 2 x = y, then 1 + y^{4} = 17 (1 + y)^{4}$
$\begin{array}{l} \Rightarrow y = \sin 2 x = - 1 / 2 \\ \Rightarrow x = 105^{\circ}, 165^{\circ}, 285^{\circ}, 345^{\circ} \end{array}$

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