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若sina+f(a)=2/3,f(a)=sin(a+π/2),求(√2sin(2a-π/4)+1)/(1+tana)的值

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/05 02:59:14
若sina+f(a)=2/3,f(a)=sin(a+π/2),求(√2sin(2a-π/4)+1)/(1+tana)的值
sina+f(a)=2/3 sina+sin(a+π/2)=2/3
sina+sin(-a+π/2)=2/3
sina+cosa=2/3 1+2sinacosa=4/9 2sinacosa=-5/9
(√2sin(2a-π/4)+1)/(1+tana)=(√2(sin2a√2/2-cos2a√2/2)+1)/(1+tana)=(sin2a-cos2a+1)/(1+tana)=
cosa(sin2a-cos2a+1)/(sina+cosa)=(2sinacos^2a+2sin^2acosa)/(sina+cosa)=
2sinacosa=-5/9