已知函数f(x)=2sinxcosx+cos2x.(1)求f()的值;(2)设α∈(0,π),f()=,求sinα的值.

已知函数f(x)=2sinxcosx+cos2x.

(1)求f()的值;

(2)设α∈(0,π),f()=,求sinα的值.

答案

解:(1)∵f(x)=sin2x+cos2x,

∴f()=sin+cos=1.

(2)∵f()=sinα+cosα=,

∴sin(α+)=,cos(α+)=±,

sinα=sin(α+-)

=××=.

∵α∈(0,π),∴sinα＞0.故sinα=.

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