已知函数f(x)满足下列关系式:(1)对于任意的x,y∈R,恒有2f(x)f(y)=f(π/2-x+y)-f(π/2-x-y) f(π/2)=1已知函数f(x)满足下列关系式:(1)对于任意的x,y∈R,恒有2f(x)f(y)=f(π/2-x+y)-f(π/2-x-y)(2)f(π/2)=1求证
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![已知函数f(x)满足下列关系式:(1)对于任意的x,y∈R,恒有2f(x)f(y)=f(π/2-x+y)-f(π/2-x-y) f(π/2)=1已知函数f(x)满足下列关系式:(1)对于任意的x,y∈R,恒有2f(x)f(y)=f(π/2-x+y)-f(π/2-x-y)(2)f(π/2)=1求证](/uploads/image/z/3503520-0-0.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%E6%BB%A1%E8%B6%B3%E4%B8%8B%E5%88%97%E5%85%B3%E7%B3%BB%E5%BC%8F%EF%BC%9A%EF%BC%881%EF%BC%89%E5%AF%B9%E4%BA%8E%E4%BB%BB%E6%84%8F%E7%9A%84x%2Cy%E2%88%88R%2C%E6%81%92%E6%9C%892f%28x%29f%28y%29%3Df%28%CF%80%2F2-x%2By%29-f%28%CF%80%2F2-x-y%29+f%28%CF%80%2F2%29%3D1%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%E6%BB%A1%E8%B6%B3%E4%B8%8B%E5%88%97%E5%85%B3%E7%B3%BB%E5%BC%8F%EF%BC%9A%EF%BC%881%EF%BC%89%E5%AF%B9%E4%BA%8E%E4%BB%BB%E6%84%8F%E7%9A%84x%2Cy%E2%88%88R%2C%E6%81%92%E6%9C%892f%28x%29f%28y%29%3Df%28%CF%80%2F2-x%2By%29-f%28%CF%80%2F2-x-y%29%EF%BC%882%EF%BC%89f%28%CF%80%2F2%29%3D1%E6%B1%82%E8%AF%81)
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