First slide

Trigonometric equations

Question

In $(- \frac{π}{2}, \frac{π}{2}), \log_{\sin θ} (\cos 2 θ) = 2$ has

Easy

A

no solution
B

a unique solution
C

two solutions
D

infinitely many solutions

Solution

$W e h a v e - \frac{π}{2} \leq θ \leq \frac{π}{2} . ∴ - 1 \leq \sin θ \leq 1, h e r e 0 < \sin θ < 1 (∵ \sin θ i s a b a s e o f \log a r i t h m) \Rightarrow 0 < θ < \frac{π}{2}$
$N o w, \log_{\sin θ} \cos 2 θ = 2 \Rightarrow \log_{\sin θ} (1 - 2 \sin^{2} θ) = 2 \Rightarrow 1 - 2 \sin^{2} θ = \sin^{2} θ \Rightarrow \sin θ = \frac{1}{\sqrt{3}} \Rightarrow θ i s u n i q u e$

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