(sinα/2+cosα/2)^2+2sin^2(π/4-α/2)=

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(sinα/2+cosα/2)^2+2sin^2(π/4-α/2)=

(sinα/2+cosα/2)^2+2sin^2(π/4-α/2)=
(sinα/2+cosα/2)^2+2sin^2(π/4-α/2)=

(sinα/2+cosα/2)^2+2sin^2(π/4-α/2)=
答案如图

(sinα/2+cosα/2)²+2sin²(π/4-α/2)
=sin²α/2+cos²α/2+2sinα/2cosα/2+1-cos[2(π/4-α/2)]
=1+sinα+1-cos(π/2-α)
=2+sinα-sinα
=2

原式=sin^2 α/2+cos^2 α/2+2sinα/2cosα/2+1-[1-2sin^2 (π/4-α/2)]
=1+sinα+1+cos(π/2-α)
=2+sinα+sinα
=2+2sinα