First slide

Multiple and sub- multiple Angles

Question

The solution of $\frac{\sqrt{5} - 1}{\sin x} + \frac{\sqrt{10 + 2 \sqrt{5}}}{\cos x} = 8, x \in (0, \frac{π}{2})$ is

Easy

A

$18^{0}, 108^{0}$
B

$36^{0}, 108^{0}$
C

$18^{0}, 54^{0}$
D

$36^{0}, 54^{0}$

Solution

$\frac{(\sqrt{5} - 1)}{4} \cos x + \frac{\sqrt{10 + 2 \sqrt{5}}}{4} \sin x = 2 \sin x . \cos x \Rightarrow \sin (x + \frac{π}{10}) = \sin 2 x$
$\Rightarrow x + \frac{π}{10} = 2 x o r x + \frac{π}{10} = π - 2 x \Rightarrow x = \frac{π}{10} o r x = \frac{3 π}{10}$

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