In the triangle ABC, lines `OA,OB` and `OC` are drawn so that angles OAB, OBC and OCA are each equal to `omega`, prove that `cotomega=cotA+cotB+cotC`

Angles A, B and C of a triangle ABC are equal to each other. Prove that DeltaABC is equilateral.

In a triangle ABC, if sin A sin (B-C)= sin c sin (A-B) , then prove that cotA, cotB, CotC are in AP.

If A,B,C are the angles of a triangle and sin^3 theta= sin (A- theta)sin (B-theta)sin (C-theta) , prove that: cot theta= cotA+cotB +cotC .

Angle A,B,C of a triangle ABC are equal to each other.Prove that ABC is equilateral.

If length of the sides of a triangle ABC are 4 cm, 5 cm and 6 cm, O is point inside the triangle ABC such that angle OBC = angle OCA = angle OAB = theta , then value of cot theta is .

In any triangle ABC prove that a^2cotA+b^2cotB+c^2cotC=(abc)/R

Bisectors of angles B and C of an isoscels triangles ABC with AB=AC intersects each other at O. prove that external angle adjacent to angleABC is equal to angleBOC .

PQ is a vertical tower having P as the foot. A,B,C are three points in the horizontal plane through P. The angles of elevation of Q from A,B,C are equal and each is equal to theta . The sides of the triangle ABC are a,b,c, and area of the triangle ABC is del . Then prove that the height of the tower is (abc) tantheta/(4)dot