Question

The value of ${\sin }^6\theta +{\cos }^6\theta +3{\sin }^2\theta {\cos }^2\theta$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is B $1$

We have
${\sin }^6\theta +{\cos }^6\theta +3{\sin }^2\theta {\cos }^2\theta ={\sin }^6\theta +{\cos }^6\theta +3{\sin }^2\theta {\cos }^2\theta ({\sin }^2\theta +{\cos }^2\theta )$
$={({\sin }^2\theta +{\cos }^2\theta )}^3=1$