Question

The value of $6\left({\sin }^6\theta +{\cos }^6\theta \right)-9\left({\sin }^4\theta +{\cos }^4\theta \right)+4$ is

Answer 1

$6\left({\sin }^6\theta +{\cos }^6\theta \right)-9\left({\sin }^4\theta +{\cos }^4\theta \right)+4=6({\sin }^2\theta +{\cos }^2\theta )({\sin }^4\theta +{\cos }^4\theta -{\sin }^2\theta {\cos }^2\theta )-9({\sin }^4\theta +{\cos }^4\theta )+4=6{\sin }^4\theta +6{\cos }^4\theta -6{\sin }^2\theta {\cos }^2\theta -9{\sin }^4\theta -9{\cos }^4\theta +4=-3({\sin }^4\theta +{\cos }^4\theta +2{\sin }^2\theta {\cos }^2\theta )+4=-3({\sin }^2\theta +{\cos }^2\theta {)}^2+4=-3+4=1$