Question

Choose the correct answer from the alternatives given :
If $co{s}^2\theta -si{n}^2\theta =\frac{1}{3}$, where $0\le \theta \le \frac{\pi }{2}$ then the value of $co{s}^4\theta -si{n}^4\theta$ is

• A. $1/3$
• B. $2/3$
• C. $1/9$
• D. $2/9$

Answer 1

The correct option is A $1/3$

$co{s}^4\theta -si{n}^4\theta$
= $(co{s}^2\theta -si{n}^2\theta )(co{s}^2\theta -si{n}^2\theta )$
= $(co{s}^2\theta -si{n}^2\theta )\times 1$
= $co{s}^2\theta -si{n}^2\theta =\frac{1}{3}$