# inequalities for integrals.

#### Hamlings

Hello,

stuck on this question, is anyone able to help?

Prove that (π /3(1 + √ 3 )) ≤ (the integral from pi/6 to pi/3 of) (1+2 sin x)/ (1 + 2 cos x) dx ≤( π / 12) (1 + √ 3 ).

Thanks

#### idontknow

$$\displaystyle \sin(x) =2T/(1+T^2 )$$ ; $$\displaystyle \cos(x)=(1-T^2 )/(1+T^2 )$$ , where $$\displaystyle T=\tan(x/2)$$ and $$\displaystyle dx=2dT/(1+T^2 )$$.
Evaluate the integral first.

topsquark

#### Hamlings

Thank you very much

idontknow