First slide

Extreme values and Periodicity of Trigonometric functions

Question

$The maximum value of y = \frac{1}{\sin^{6} x + \cos^{6} x}$

Easy

A

4
B

6
C

3
D

2

Solution

We have
$\begin{array}{l} \sin^{6} x + \cos^{6} x = 1 - 3 \sin^{2} x \cos^{2} x \\ = 1 - \frac{3}{4} \sin^{2} 2 x \\ \Rightarrow \frac{1}{\sin^{6} x + \cos^{6} x} = \frac{4}{4 - 3 \sin^{2} 2 x} \\ ∴ y_{\max} = \frac{4}{4 - 3 (1)} = 4 \end{array}$

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