Question

It is a triangle ABC, \(\begin{vmatrix} 1 &a & b \\[0.3em] 1 &c &a \\[0.3em] 1 & b &c \end{vmatrix}\) = 0

then find the value of sin²A+ sin²B+ sin²C

Answer 1

= c² - ab - ac + a² + b² - bc

= a² + b² + c² - ab - bc - ac