请问！数学题！

samuria

if given a , b ,c are angles of triangle.
please prove cos^2(a)+cos^(b)+cos^2(c)=1-2cos(a)cos(b)cos(c)
请问如何做？

mathlim

cos²a + cos²b + cos²c
= (1+cos2a)/2 + (1+cos2b)/2 + cos²[180°-(a + b)]
= 1 + (cos2a+cos2b)/2 + [-cos(a + b)]²
= 1 + cos(a+b) cos(a-b) + cos²(a+b)
= 1 + [cos(a+b) + cos(a-b)] cos(a+b)
= 1 - 2cosa cosb cosc