First slide

Trigonometric equations

Question

If $\sin^{2} (x + π / 4) + \sqrt{3} \cos 2 x > 0,$ then

Moderate

A

$\cos (2 x - π / 6) > - 1 / 2$
B

$\sin (2 x - π / 6) < - 1 / 2$
C

$\sin (2 x - π / 6) > - 1 / 2$
D

$\cos (2 x - π / 6) < - 1 / 2$

Solution

$\begin{array}{l} 2 \sin^{2} (x + π / 4) + \sqrt{3} \cos 2 x > 0 \\ \Rightarrow 1 - \cos (2 x + π / 2) + \sqrt{3} \cos 2 x > 0 \\ \Rightarrow \frac{1}{2} \sin 2 x + \frac{\sqrt{3}}{2} \cos 2 x > - \frac{1}{2} \\ \Rightarrow \cos (2 x - π / 6) > - \frac{1}{2} \end{array}$

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