求高手帮忙化简f(x)=(sin2x+cos2x+1)/(根号2*sin(π/4+x))+cos(π/2+π)

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求高手帮忙化简f(x)=(sin2x+cos2x+1)/(根号2*sin(π/4+x))+cos(π/2+π)
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求高手帮忙化简f(x)=(sin2x+cos2x+1)/(根号2*sin(π/4+x))+cos(π/2+π)
求高手帮忙化简f(x)=(sin2x+cos2x+1)/(根号2*sin(π/4+x))+cos(π/2+π)

求高手帮忙化简f(x)=(sin2x+cos2x+1)/(根号2*sin(π/4+x))+cos(π/2+π)
化简f(x)=[(sin2x+cos2x+1)/(√2)sin(π/4+x)]+cos(π/2+π)
f(x)=[(2sinxcosx+cos²x-sin²x+1)/(cosx+sinx)]+0
=[2sinxcosx+2cos²x)/(cosx+sinx)=2cosx(sinx+cosx)/(cosx+sinx)=2cosx.