已知(1+tanx)/(1-tanx) =3+2根号2 ,求(sin^2 x+根号2sinx*cosx-cos^2 x)/(sin^2 x+2cos^2 x) 的值
问题描述:
已知(1+tanx)/(1-tanx) =3+2根号2 ,求(sin^2 x+根号2sinx*cosx-cos^2 x)/(sin^2 x+2cos^2 x) 的值
答
(1+tanx)/(1-tanx) =3+2根号2 ,
解得tanx=√2/2.
(sin^2 x+根号2sinx*cosx-cos^2 x)/(sin^2 x+2cos^2 x)
=(tan^2x+√2tanx-1)/(tan^2x+2)
=(1/2+1-1)/(1/2+2)
=1/5.