cos2x/(1+sin2x)=1/5 求tanx
cos2x/兆橡(1+sin2x)=1/5
(cos^2x-sin^2x)/(sinx+cosx)^2=1/5
分子分如轮母同除以cos^2x:
(1-tan^2x)/(tanx+1)^2=1/5
5(1-tan^2x)=tan^2x+2tanx+1
3tan^2x+tanx-2=0
(3tanx-2)(tanx+1)=0
tanx=2/3或tanx=-1.
tanx=-1时,x=180k-45,2x=360-90,cos2x=0,不符题族橡旁意,舍.
所以,tanx=2/3