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

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

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

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.

Prove that the area of a right angled triangle of a given hypotenuse is maximum when the triangle is isosceles.

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.

/_\PBC and /_\ QBC are two isosceles triangles on the same side of the some base. Show that the PQ is the right bisector of BC.

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

In an isosceles triangle ABC if AB = AC= 15 cm and BC =18 cm, find the values of cos /_ABC and sin /_ABC .

In triangle ABC,right-angled at B ,if tan A= 1/ sqrt3 , find the value of sin A cos C+cos A sin C