SOLUTION: Prove: Cos4x = 8Cos^4(x) - 8Cos^2(x) + 1 Thank you in advance

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Question 927208: Prove:
Cos4x = 8Cos^4(x) - 8Cos^2(x) + 1
Thank you in advance
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
to prove cos%284x%29+=+8cos%5E4%28x%29+-+8cos%5E2%28x%29+%2B+1, start with right side

8cos%5E4%28x%29+-+8cos%5E2%28x%29+%2B+1

=8cos%5E2%28x%29%28cos%5E2%28x%29+-+1%29+%2B+1

=8cos%5E4%28x%29+-+8cos%5E2%28x%29+%2B+1

=8cos%5E2%28x%29%28cos%5E2%28x%29+-+1%29+%2B+1 .........substitute cos%5E2%28x%29=1-sin%5E2%28x%29

=8cos%5E2%28x%29%281-sin%5E2%28x%29+-+1%29+%2B+1

=8cos%5E2%28x%29%28-sin%5E2%28x%29+%29+%2B+1

=1-8sin%5E2%28x%29cos%5E2%28x%29 .................substitute sin%5E2%28x%29cos%5E2%28x%29=%281%2F4%29+sin%5E2%282x%29

=1-8%281%2F4%29sin%5E2%282x%29

=1-2sin%5E2%282x%29 ..............substitute sin%5E2%282x%29+=%281%2F2%29%281-cos%284x%29%29

=1-2%281%2F2%29%281-cos%284x%29%29

=1-+%281-cos%284x%29%29

=1-+1%2Bcos%284x%29

=cos%284x%29 ...we came to the left side