Question

${\sin }^6\theta +{\cos }^6\theta +3{\sin }^2\theta .{\cos }^2\theta$ is

• A. 0
• B. -1
• C. 1
• D. 2

Answer 1

The correct option is C 1

We have,
$={\sin }^6\theta +{\cos }^6\theta +3{\sin }^2\theta .{\cos }^2\theta$
$={\sin }^6\theta +{\cos }^6\theta +3{\sin }^2\theta .{\cos }^2\theta ({\sin }^2\theta +{\cos }^2\theta )$
$=({\sin }^2\theta {)}^3+({\cos }^2\theta {)}^3+3{\sin }^2\theta .{\cos }^2\theta ({\sin }^2\theta +{\cos }^2\theta )$
$=({\sin }^2\theta +{\cos }^2\theta {)}^3$
$=1^3$
$=1$
Hence, this is the answer.