SOLUTION: prove that cos4theta-4cos2theta+3 is 8sin^4theta

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Question 1160082: prove that cos4theta-4cos2theta+3 is 8sin^4theta
Answer by MathLover1(20850) About Me  (Show Source):
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cos%284theta%29-4cos%282theta%29%2B3+=+8sin%5E4%28theta%29
manipulate left side
cos%284theta%29-4cos%282theta%29%2B3.........since

then we have
2cos%5E2%282theta%29-1-4cos%282theta%29%2B3
%282cos%5E2%282theta%29-4cos%282theta%29%29%2B2
2cos%282theta%29%28cos%282theta%29-2%2B1%2Fcos%282theta%29%29
2cos%282theta%29%28%28cos%5E2%282theta%29-2cos%282theta%29%2B1%29%2Fcos%282theta%29%29..........simplify
2%28cos%5E2%282theta%29-2cos%282theta%29%2B1%29+
2%28cos%282theta%29-1%29+%5E2...........since cos%282theta%29=cos%28theta%2Btheta%29=cos%5E2%28theta%29+-+sin%5E2%28theta%29
2%28cos%5E2%28theta%29+-+sin%5E2%28theta%29-1%29+%5E2.........use cos%5E2%28theta%29=1-sin%5E2%28theta%29
2%281-sin%5E2%28theta%29+-+sin%5E2%28theta%29-1%29+%5E2
2%28-2sin%5E2%28theta%29+%29+%5E2
2%284sin%5E4%28theta%29+%29
8sin%5E4%28theta%29-> proven