a, b, c are the lengths of three sides of a triangle ABC. If a, b, c…

Question

a, b, c are the lengths of three sides of a triangle ABC. If a, b, c are related by the relation a2 + b2 + c2 = ab + bc + ca, then the value of (sin2A + sin2B + sin2C) is?

Accepted Answer

Option D. 9/4. Answer & Solution Answer: Option D Solution: & a^2 + b^2 + c^2 = ab + bc + ca & a^2 + b^2 + c^2 - ab - bc - ca = 0 & 2a^2 + 2b^2 + 2c^2 - 2ab - 2bc - 2ca = 0 & a^2 + b^2 - 2ab + b^2 + c^2 - 2bc + c^2 + a^2 - 2ca = 0 & ( a - b )^2 + ( b - c )^2 + ( c - a )^2 = 0 & a = b = c & ABC…