Chapter 14.5, Problem 33PPS

To determine

To Solve :The given value is $3{\sin }^2\theta ={\cos }^2\theta ;0\le \theta \le \frac{\pi }{2}$

Answer to Problem 33PPS

  $\theta =\frac{\pi }{2}$

Explanation of Solution

Given information :

We know that, the given equation is $3{\sin }^2\theta ={\cos }^2\theta ;0\le \theta \le \frac{\pi }{2}.$

Formula Used:

  ${\cos }^2\theta =1-{\sin }^2\theta$

Calculation :

The given equation is

  $\begin{array}{l}3{\sin }^2\theta =1-{\sin }^2\theta ;0\le \theta \le \frac{\pi }{2}\\ 4{\sin }^2\theta =1\\ {\sin }^2\theta =\frac{1}{4}\\ \sin \theta =\pm \frac{1}{2}\\ As0\le \theta \le \frac{\pi }{2}\\ \sin \theta =\frac{1}{2}\\ \theta =\frac{\pi }{6}\end{array}$