已知1+tan/1-tan=3+2根号2,求（sin^2x+根号2sinxcosx-cos^2）/（sin^2+2cos^2）的值

题目

已知1+tan/1-tan=3+2根号2,求（sin^2x+根号2sinxcosx-cos^2）/（sin^2+2cos^2）的值

答案

(1+tanx)/(1-tanx)=3+2根号21+tanx = (3+2根号2) - (3+2根号)tanx2(2+根号2)tanx = 2(根号2+1）tanx = (根号2+1) / (2+根号2) = 根号2/2(sin^2x+根号2sinxcosx-cos^2）/（sin^2x+2cos^2x）分子分母同除以cos^2x：= (...