Question

How do I solve cos x> 1/2 sin x?

Answer 1

Divide both sides by $\dfrac12\cos x$:

$\dfrac{\cos x}{\frac12\cos x}>\dfrac{\frac12\sin x}{\frac12\cos x}\implies2>\dfrac{\sin x}{\cos x}=\tan x$

If $-\dfrac\pi2$, then

$\tan x$

and more generally, for any integer $n$,

$n\pi-\dfrac\pi2$