Question

Solve for $x:4{\sin }^{2}x-4\cos x=1$.

Answer 1

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

$⟹4(1-{\cos }^{2}x)-4\cos x=1$

$⟹4-4{\cos }^{2}x-4\cos x=1$

$⟹4{\cos }^{2}x+4\cos x-3=0$

$⟹4{\cos }^{2}x+6\cos x-2\cos x-3=0$

$⟹(2\cos x-1)(2\cos x+3)=0$

$⟹\cos x=\frac{1}{2}$

$⟹x={60}^{{}^{\circ }}$