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已知cos(π-x)=3/5,x∈[0,π),则sin(2x-π/4)=
人气:445 ℃ 时间:2020-06-27 11:58:37
解答
∵cos(π-x)=3/5
∴cosx=-3/5
sinx=4/5
∴sin2x=2sinx*cosx=-24/25
cos2x=(cosx)平方-(sinx)平方=-7/25
∵sin(2x-π/4)
=sin2xcosπ/4-cos2xsinπ/4
=根号2/2*sin2x-根号2/2*cos2x
=根号2/2(sin2x-cos2x)
=-17根号2/50
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