化简:(4cos^4a-4cos^2+1)/[2tan(π/4-a)sin^2(π/4+a)]

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化简:(4cos^4a-4cos^2+1)/[2tan(π/4-a)sin^2(π/4+a)]
化简:(4cos^4a-4cos^2+1)/[2tan(π/4-a)sin^2(π/4+a)]

化简:(4cos^4a-4cos^2+1)/[2tan(π/4-a)sin^2(π/4+a)]
=(2cos2a-1)2=[2tan(π/4-a)*cos2(π/4-a)]
=cos22a/[2sin(π/4-a)cos(π/4-a)]
=cos22a/sin(π/2-2a)
=cos22a/cos2a
=cos2a

(4cos^4a-4cos^2+1)/[2tan(π/4-a)sin^2(π/4+a)]
=(2cos^2a-1)^2/[sin^2(π/4+a)2sin(π/4-a)/cos(π/4-a)]
=(cos2a)^2/[2sin^2(π/4+a)sin(π/4-a)/sin(π/2-(π/4-a)]
=(cos2a)^2/[2sin(π/4+a)sin(π/4-a)] 积化...

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(4cos^4a-4cos^2+1)/[2tan(π/4-a)sin^2(π/4+a)]
=(2cos^2a-1)^2/[sin^2(π/4+a)2sin(π/4-a)/cos(π/4-a)]
=(cos2a)^2/[2sin^2(π/4+a)sin(π/4-a)/sin(π/2-(π/4-a)]
=(cos2a)^2/[2sin(π/4+a)sin(π/4-a)] 积化和差
=(cos2a)^2/[cos((π/4+a)-(π/4-a))-cos((π/4+a)+π/4-a))]
=(cos2a)^2/[cos2a-cosπ/2]
=(cos2a)^2/cos2a
=cos2a

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