tan2Θ=-2√2,π/4

题目

tan2Θ=-2√2,π/4

答案

π/4tana<0
tan2a=-2√2
=(2tana)/(1-tan^2 a)
tana=-√2/2
=sina/cosa
sina=-√2/2cosa
(2cos^2a/2-sina-1)/√2sin(π/4+a)
=(1+cosa-sina-1)/(sina+cosa)
=[-(sina-cosa)]/(sina+cosa)
=3+2√2