已知f(x)=sinx+cosx,f'(x)=3f(x),f'(x)为f(x)的导数,则(sin^2x-3)/(cos^2+1)=?
问题描述：
已知f(x)=sinx+cosx,f'(x)=3f(x),f'(x)为f(x)的导数,则(sin^2x-3)/(cos^2+1)=?
答
f'(x)=cosx-sinx=3(sinx+cosx)
=>4sinx=-2cosx
=>cosx=-2sinx
sin^2x+cos^2x=1
=>sin^2x=1/5
cos^2x=4/5
=>(sin^2x-3)/(cos^2x+1)=-16/5/9/5=-16/9