sin^2(π/4 +x)

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sin^2(π/4 +x)
sin^2(π/4 +x)

sin^2(π/4 +x)
sin^2(π/4 +x)
=[1-cos2(π/4 +x)]/2
=[1-cos(π/2 +2x)]/2
=1/2+sin2x/2
运用公式
Cos2A=CosA^2-SinA^2=1-2SinA^2

sin^2(π/4 +x)
=[1-cos(π/2+2x)]/2
=[1-(cosπ/2cos2x-sinπ/2sin2x)]/2
=[1-(0-sin2x)]/2
=(1/2)sin2x+1/2

这种单有平方的，一般就用二倍角公式，即将原式化为与（π/2 +2x）的关系，通过Cos2A=1-2SinA^2，代入原式即得cos2A，解得为（1+sin2x）/2

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