Posted by Anand on Saturday, January 26, 2013 at 2:19am.
I assume you mean
cos^2 A + cos^2 B + cos^2 C
cos A = 0 this is a right triangle with right angle at A so cos^2 A =0
so
cos B = b/a
cos C = c/a
b = a cos B
c = a cos C
but b^2 + c^2 = a^2
a^2 cos^2 B + a^2 cos^2 C = a^2
so
cos^2 B + cos^2 C = 1
so
cos^2 A + cos^2 B + cos^2 C = 1
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