SOLUTION: Use the power-reducing formulas as many times as possible to rewrite the expression in terms of the first power of the cosine.
sin^2(4x)cos^2(4x)
I am confused about how to red
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-> SOLUTION: Use the power-reducing formulas as many times as possible to rewrite the expression in terms of the first power of the cosine.
sin^2(4x)cos^2(4x)
I am confused about how to red
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Question 889804: Use the power-reducing formulas as many times as possible to rewrite the expression in terms of the first power of the cosine.
sin^2(4x)cos^2(4x)
I am confused about how to reduce this problem. Answer by charu91(7) (Show Source):
You can put this solution on YOUR website! cos2A=2cos^2(A)-1
cos^(A)=(cos2A+1)/2
so cos^2(4x) can be written as cos^2(4x)=(1+cos8x)/2
cos2A=1-2sin^2(A)
sin^2(A)=(1-cos2A)/2
sin^2(4x)=(1-cos8x)/2
substituting these in eqn sin^2(4x)cos^2(4x) we get ((1-cos8x)/2)((1+cos8x)/2)=(1-cos^2(8x))/4
=(1-(cos16x+1)/2)/4
=1/4-(1/8*cos16x)-1/8
=1/8-(1/8*cos16x)
=1/8*(1-cos16x)
answer to the question
sin^2(4x)cos^2(4x) = 1/8*(1-cos16x)
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