First slide

Compound angles

Question

If $2 \cos x + 2 \cos 3 x = \cos y, 2 \sin x + 2 \sin 3 x = \sin y$ then the value of $\cos 2 x$ of

Moderate

A

– 7/8
B

1/8
C

– 1/8
D

7/8

Solution

$\cos y = 2 \times 2 \cos 2 x \cos x$
$\sin y = 2 \times 2 \sin 2 x \cos x$
$\Rightarrow 1 = \cos^{2} y + \sin^{2} y = 16 \cos^{2} x$
So $\cos 2 x = 2 \cos^{2} x - 1 = - 7 / 8$

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