First slide

Extreme values of trigonometric functions in trigonometry

Question

If $|\cos θ \{\sin θ + \sqrt{\sin^{2} θ + \sin^{2} α}\}| \leq k$ then the value of k is

Moderate

A

$\sqrt{1 + \cos^{2} α}$
B

$\sqrt{1 + \sin^{2} α}$
C

$\sqrt{2 + \sin^{2} α}$
D

$\sqrt{2 + \cos^{2} α}$

Solution

$Let u = \cos θ \{\sin θ + \sqrt{\sin^{2} θ + \sin^{2} α}\}$
$\begin{array}{l} or (u - \sin θcos θ)^{2} = \cos^{2} θ (\sin^{2} θ + \sin^{2} α) \\ or u^{2} \tan^{2} θ - 2 utan θ + u^{2} - \sin^{2} α = 0 \end{array}$
Since tan $θ$ is real, we have
$\begin{array}{ll} 4 u^{2} - 4 u^{2} (u^{2} - \sin^{2} α) \geq 0 \\ or u^{2} \leq 1 + \sin^{2} α \\ or | u | \leq \sqrt{1 + \sin^{2} α} \end{array}$

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