Question

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

Answer 1

Divide both sides by
`\frac12\cos x`:

`(\cos x)/(\frac12\cos x)>(\frac12\sin x)/(\frac12\cos x)\implies2>(\sin x)/(\cos x)=\tan x`

If
`-\frac\pi2<x<\frac\pi2`, then

`\tan x<2\implies-\frac\pi2<x<\tan^(-1)2`

and more generally, for any integer
`n`,

`n\pi-\frac\pi2<x<n\pi+\tan^(-1)2`