Question

What is the value of ${\sin }^6\theta +{\cos }^6\theta +3{\sin }^2\theta {\cos }^2\theta$ ?

Answer 1

$\because {\sin }^2\theta +{\cos }^2\theta =1$
$\therefore {({\sin }^2\theta +{\cos }^2\theta )}^3=1^3=1$
$\Rightarrow {\sin }^6\theta +{\cos }^6\theta +3{\sin }^2\theta {\cos }^2\theta ({\sin }^2\theta +{\cos }^2\theta )$
$=1$
$\Rightarrow {\sin }^6\theta +{\cos }^6\theta +3{\sin }^2\theta {\cos }^2\theta =1$