若tanα=2,则sin2α-cos2α/1+cos²α

问题描述:

若tanα=2,则sin2α-cos2α/1+cos²α

tana=2,sina/cosa=2,sina=2cosa
sin2a-cos2a=2sinacosa-cos^2a+sin^2a=4cos^2a-cos^2a+4cos^2a=7cos^2a
1+cos^2a=sin^2a+2cos^2a=6cos^2a
所以,原式=7cos^2a/6cos^2a=7/6

(sin2α-cos2α)/(1+cos²α)= (2sinαcosα-cos²α+sin²α)/(sin²α+2cos²α)分子分母同除以cos²α:= (2tanα-1+tan²α)/(tan²α+2)= (2*2-1+2²)/(2²+2)= 7/6...