SOLUTION: If A + B + C = 180 then prove that Cos^2 A + cos^2 B + 2cosAcosBcosC=sin^2 C

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Question 1046463: If A + B + C = 180 then prove that
Cos^2 A + cos^2 B + 2cosAcosBcosC=sin^2 C
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
C+=+180%5Eo+-%28+A+%2BB%29
===> cosC+=+cos%28180%5Eo+-+%28A+%2BB%29%29+=+-cos+%28A%2BB%29+=+sinAsinB+-+cosAcosB
===>
=
=
=cos%5E2%28A%29sin%5E2%28B%29+%2B+cos%5E2%28B%29sin%5E2%28A%29+%2B+2sinA+cosA+sinB+cosB++
= %28sinAcosB+%2B+cosAsinB%29%5E2
= +sin%5E2%28A%2BB%29
= +sin%5E2%28180%5Eo+-+%28A%2BB%29%29+=+sin%5E2%28C%29.
And that's it...