Question

33. Prove that, for a triangle ABC,
if cot A + cot B = 2cotC, then AC2 + BC2 = 2AB2.​

Answer 1

Answer:

In any triangle

cotA=(b^2+c^2-a^2)÷(4×area)

cotB=(c^2+a^2-b^2)÷(4×area)

cotC=(a^2+b^2-c^2)÷(4×area)

Substitute in ur equation

cotA+cotB=2cotC

U will get 2c^2=b^2+a^2

2(AB)^2=AC^2+BC^2