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.

If cosines of two angles of a triangle are inversely proportional to the opposite sides, show that the triangle is either isosceles or right-angled.

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

In /_\ABC ,a/cosA=b/cosB=c/cosC.Show that the triangle is equilateral.

In the triangle ABC,AB=p^2-q^2,BC=p^2+q^2 and CA=2pq then prove that triangleABC is right angled.Which of the angles of the triangle is right angle?

Show that in a triangle ABC, a^3sin(B-C)+b^3sin(C-A)+c^3sin(A-B)=0

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

The length of the sides of a triangle are ax-by , ay+bx and sqrt((a^2+b^2)(x^2+y^2)) . Show that it is a right angled triangle.

If cosines of two angles of a triangle are proportional to the opposite sides, show that the triangle is isosceles

The length of the sides of a triangle are a+b , ab-1 and sqrt((a^2+1)(b^2+1)) . Show that it is a right angled triangle.

In the triangle ABC, BC+CA=m^2+2mn-n^2 , CA+AB=(m+n)^2 and AB+BC=2m^2 . Show that it is a right angled triangle.