math
posted by Anonymous .
Prove the identity: cos^4(x)sin^4(x)=12sin^2(x).with explanation
im confused on this one cause of the 4th power of the sine. does this mean that we put it in the calculator 4 times? and what exactly does it mean by prove the identity does it mean like make sure both sides equal each other?

cos ^ 4( x )  sin ^ 4 ( x ) =
[ cos ^ 2 ( x ) ] ^ 2  [ sin ^ 2 ( x ) ] ^ 2 =
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Remark:
a ^ 2  b ^ 2 = ( a + b ) * ( a  b )
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= [ cos ^ 2 ( x ) + sin ^ 2 ( x ) ] *
[ cos ^ 2 ( x )  sin ^ 2 ( x ) ] =
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Remark:
cos ^ 2 ( x ) + sin ^ 2 ( x ) = 1
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= 1 * [ cos ^ 2 ( x )  sin ^ 2 ( x ) ] =
cos ^ 2 ( x )  sin ^ 2 ( x ) =
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Remark:
cos ^ 2 ( x ) = 1  sin ^ 2 ( x )
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= 1  sin ^ 2 ( x )  sin ^ 2 ( x ) =
1  2 sin ^ 2 ( x )