First slide

Trigonometric equations

Question

Number of solution of $\sec x \cos 5 x + 1 = 0$ where $0 < x \leq \frac{π}{2}$

Moderate

A

4
B

1
C

3
D

2

Solution

$W e h a v e s e c x \cos 5 x + 1 = 0 \Rightarrow \frac{1}{\cos x} \cos 5 x + 1 = 0 \Rightarrow \cos 5 x + \cos x = 0$
$\Rightarrow 2 \cos 3 x c o s 2 x = 0 \Rightarrow \cos 3 x = 0, \cos 2 x = 0 \Rightarrow 3 x = (2 n + 1) \frac{π}{2}, 2 x = (2 n + 1) \frac{π}{2} \Rightarrow x = \frac{π}{6}, \frac{π}{4} (∵ 0 < x < \frac{π}{2} a s e q u a t i o n i s n o t d e f i n e d f o r x = \frac{π}{2})$

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