设函数f(x)=sinx+cosx,f'(x)是f(x)的导数,若f(x)=2f'(x)则sin^2x-sin2x/cos^2x的值是多少

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设函数f(x)=sinx+cosx,f'(x)是f(x)的导数,若f(x)=2f'(x)则sin^2x-sin2x/cos^2x的值是多少

设函数f(x)=sinx+cosx,f'(x)是f(x)的导数,若f(x)=2f'(x)则sin^2x-sin2x/cos^2x的值是多少
设函数f(x)=sinx+cosx,f'(x)是f(x)的导数,若f(x)=2f'(x)
则sin^2x-sin2x/cos^2x的值是多少

设函数f(x)=sinx+cosx,f'(x)是f(x)的导数,若f(x)=2f'(x)则sin^2x-sin2x/cos^2x的值是多少
f'(x)是f(x)的导数f'(x)=cosx-sinx;
f(x)=2f'(x) 则sinx+cosx=2*(cosx-sinx)
所以cosx=3sinx
tanx=1/3 x=arctan1/3
sin^2x-sin2x/cos^2x=sin^2x-cosx*sinx/cos^2x=sin^2x-sinx/cosx=sin(arctan1/2)^2-1/3