已知cos(x-派/4)=根2/10,x属于(派/2,3派/4),求cos(2x+派/3)的值
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![已知cos(x-派/4)=根2/10,x属于(派/2,3派/4),求cos(2x+派/3)的值](/uploads/image/z/14763488-32-8.jpg?t=%E5%B7%B2%E7%9F%A5cos%28x-%E6%B4%BE%2F4%29%3D%E6%A0%B92%2F10%2Cx%E5%B1%9E%E4%BA%8E%28%E6%B4%BE%2F2%2C3%E6%B4%BE%2F4%29%2C%E6%B1%82cos%282x%2B%E6%B4%BE%2F3%29%E7%9A%84%E5%80%BC)
已知cos(x-派/4)=根2/10,x属于(派/2,3派/4),求cos(2x+派/3)的值
已知cos(x-派/4)=根2/10,x属于(派/2,3派/4),求cos(2x+派/3)的值
已知cos(x-派/4)=根2/10,x属于(派/2,3派/4),求cos(2x+派/3)的值
已知,cos(x-π/4)=√2/10,x属于(π/2,3π/4),求cos(2x+π/3)的值
cos(x-π/4)=√2/2(cosx+sinx)=√2/10 ,sinx+cosx=1/5 ,1+sin2x=1/25,sin2x=-24/25 ,cos2x=-7/25
cos(2x+π/3)=1/2cos2x-√3/2sin2x=(-7/50)+24√3/50=(24√3-7)/50
∵cos(x-π/4)=√2/10∴cosx+sinx=1/5∴sin2x=-24/25∵x∈[π/2,3π/4]∴2x∈[π,3π/2]∴cos2x=-7/25
∴cos(2x+π/3)=(1/2)cos2x-(√3/2)sin2x=(24√3-7)/50