已知2sinx=cosx,求cos2x+cos2x+1/cos^2x的值.

题目

已知2sinx=cosx,求cos2x+cos2x+1/cos^2x的值.

答案

已知2sinx=cosx,
即tanx=1/2
所以
cos2x+(cos2x+1)/cos^2x
=cos2x+ 2cos²x/cos²x
=cos2x+2
=(1-tan²x)/(1+tan²x)+2
=(1-1/4)/(1+1/4)
=-3/5