If` sin^2A + sin^2B= sin^2 C`,show that `/_\ABC` is right-angled.

If cot (A/2)=(b+c)/a.show that /_\ABC is right angled.

In an isosceles triangle ABC if AC=BC and AB^2 = 2AC^2 , prove that /_C is a right angle.

In triangle ABC, a sin A= b sin B. Show that the triangle is isosceles.

If A + B + C= 1 80^@ and sin(A+C/2)=n sin (C/2) ,show that tan(A/2)tan(B/2)=(n-1)/(n+1)

If cos^2alpha-sin^2alpha=tan^2beta ,show that cos^2beta-sin^2beta=tan^2alpha

If PB and AQ are the medians of a ∆ABC right angled at C. Prove that 4BP^2 = 4 BC^2 + AC^2

If PB and AQ are the medians of a ∆ABC right angled at C. Prove that 4AQ^2 = 4 AC^2 + BC^2

If PB and AQ are the medians of a ∆ABC right angled at C. Prove that 4 (AQ^2 + BP^2) = 5 AB^2

If in triangle ABC , (a^2+b^2)sin(A-B)=(a^2-b^2)sin(A+B) ,show that the triangle is either'isosceles or right angled.

Prove any one of the following : sin^2A+sin^2B+sin^2C=2+2cos A cos Bcos C when A+B+C=pi .