First slide

Trigonometric equations

Question

$\cos (\sin x) = \frac{1}{\sqrt{2}}$ then $x$ must lie in the interval :

Moderate

A

$(\frac{π}{4}, \frac{π}{2})$
B

$(\frac{- π}{4}, 0)$
C

$(π, \frac{3 π}{2})$
D

$(\frac{π}{2}, π)$

Solution

$\begin{array}{l} \cos (\sin x) = \frac{1}{\sqrt{2}} = \cos \frac{π}{4} \\ \Rightarrow \sin x = 2 n π \pm \frac{π}{4}, n \in Ι \\ \Rightarrow \sin x = \pm \frac{π}{4} (∵ - 1 \leq \sin x \leq 1) \\ ∴ x \in (\frac{π}{4}, \frac{π}{2}), (\frac{π}{2}, π) a n d (π, \frac{3 π}{2}) \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App