求y=sinx+2sinxcosx-cosx的化简
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y=sinx+2sinxcosx-cosx
=(sinx-cosx)+[1-(sinx-cosx)²]/2
=-(1/2)(sinx-cosx)²+(sinx-cosx)+1/2
=-(1/2)[√2sin(x-π/4)]²+√2sin(x-π/4)+1/2
=-sin²(x-π/4)+√2sin(x-π/4)+1/2
=(sinx-cosx)+[1-(sinx-cosx)²]/2
=-(1/2)(sinx-cosx)²+(sinx-cosx)+1/2
=-(1/2)[√2sin(x-π/4)]²+√2sin(x-π/4)+1/2
=-sin²(x-π/4)+√2sin(x-π/4)+1/2
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