Question

tan(45+a)=1/2,求tana和(sin2a-cos^2a)/cos2a

Answer 1

tan(45+a)=1/2
(tan45+tana)/(1-tan45tana)=1/2
(1+tana)/(1-tana)=1/2
2(1+tana)=1-tana
3tana=-1
tana=-1/3

(sin2a-cos^2a)/cos2a
=(2sinacosa-cos^2a)/(cos^2a-sin^2a)分子分母同时除以cos^2a
=(2sinacosa/cos^2a-cos^2a/cos^2a)/(cos^2a/cos^2a-sin^2a/cos^2a)
=(2sina/cosa-1)/(1-sin^2a/cos^2a)
=(2tana-1)/(1-tan^2a)
=[2*(-1/3)-1]/[1-(-1/3)^2]
=(-5/3)/(8/9)
=-5/3*9/8
=-15/8

Answer 2

tan(45+a)=1/2
(1+tana)/(1-tana)=1/2
2+2tana=1-tana
3tana=-1
tana=-1/3

(sin2a-cos^2a)/cos2a
(2sinacosa-cos²a)/(cos²a-sin²a)
上下同时除以cos²a得
[2tana-1]/[1-tan²a]
=(-2/3-1)/(1-1/9)
=(-5/3)/(8/9)
=-15/8

Answer 3

tana=-1/3 (sin2a-cos^2a)/cos2a=-15/8
利用倍角展开

Answer 4

tana=1/3
(sin2a-cos^2a)/cos2a=-3/8