Math Help - Inequality trigonometric

1. Inequality trigonometric

Let $ABC$ be a triangle. Prove that:

$\frac{sinA.sinB}{sin^{2}\frac{C}{2}}+\frac{sinB.sinC}{sin^{2}\frac{A}{2}}+\frac{sinC.sinA}{sin^{2}\frac{B}{2}}\geq 9$

2. Re: Inequality trigonometric

Originally Posted by BUZZ
Let $ABC$ be a triangle. Prove that:

$\frac{sinA.sinB}{sin^{2}\frac{C}{2}}+\frac{sinB.sinC}{sin^{2}\frac{A}{2}}+\frac{sinC.sinA}{sin^{2}\frac{B}{2}}\geq 9$
Hint:

$A+B+C=180^{\circ}$

3. Re: Inequality trigonometric

Originally Posted by Also sprach Zarathustra
Hint:

$A+B+C=180^{\circ}$
Nice
Originally Posted by BUZZ
Let $ABC$ be a triangle. Prove that:

$\frac{sinA.sinB}{sin^{2}\frac{C}{2}}+\frac{sinB.sinC}{sin^{2}\frac{A}{2}}+\frac{sinC.sinA}{sin^{2}\frac{B}{2}}\geq 9$
I think I've got it. Care to share your results so that we can compare? I'd say it's only proper, seeing as you just plopped this down without showing any work as your first post on MHF...