Inequality trigonometric

**BUZZ** · August 3rd 2011, 10:28 AM

Let $ABC$ be a triangle. Prove that:

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

**Also sprach Zarathustra** · August 3rd 2011, 10:34 AM

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:

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

**TheChaz** · August 3rd 2011, 10:42 AM

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...

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