Question

Solve for $x:{\cos }^{4}x+{\sin }^{4}x=\frac{7}{2}\sin x\cos x$.

Answer 1

${\cos }^{4}x+{\sin }^{4}x=\frac{7}{2}\sin x\cos x$

$1-2\sin x\cos x=\frac{7}{2}\sin x\cos x$

$1=\frac{11}{4}\sin 2x$

$x=\frac{1}{2}{\sin }^{-1}\frac{4}{11}$