SOLUTION: if A and B are supplementary angles , prove that cos ^ 2 A - cos ^ 2 B = 0

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Question 1011313: if A and B are supplementary angles , prove that cos ^ 2 A - cos ^ 2 B = 0

Answer by MathLover1(20850) About Me  (Show Source):
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if A and B are supplementary angles , prove that cos+%5E+2+%28A%29+-+cos+%5E+2+%28B%29+=+0
Supplementary angles add up to 180°:
A+%2BB=180=>A+=180-B
then cos+%5E+2+%28A%29+-+cos+%5E+2+%28B%29+=+0+ will be

cos+%5E+2+%28180-B%29+-+cos+%5E+2+%28B%29+=+0+
since
cos%5E2%28180-B%29+=+%28cos%28180%29+cos%28B%29%2Bsin%28180%29+sin%28B%29%29%5E2
and
sin%28180%29+=0
cos+%28180%29+=+-1
we have:
cos%5E2%28180-B%29+=+%28-1%2A+cos%28B%29%2B0%2A+sin%28B%29%29%5E2
cos%5E2%28180-B%29+=cos%5E2%28B%29
so,substitute it in
cos+%5E+2+%28180-B%29+-+cos+%5E+2+%28B%29+=+0 and it will be
cos%5E2%28B%29+-+cos+%5E+2+%28B%29+=+0
0=+0+