Question

已知sin(a)=cos(2a),a属于(π/2,π) 求tan(a)

Answer 1

sina=1-2sin²a,
2sin²a+sina -1=0,
因为a∈(π/2,π),sina>0
从而解得 sina=1/2,
a=5π/6
tana=tan(5π/6)=-tan(π/6)=-√3/3

Answer 2

sina=cos2a
sina=1-2sin²a
2sin²a+sina-1=0
(sina+1)(2sina-1)=0
sina=-1 sina=1/2
a属于(π/2,π)
取sina=1/2
a=5π/6
tana=-√3/3

Answer 3

sina=1-2sin²a
2sin²a+sina-1=0
(sina+1)(2sina-1)=0
sina=-1, sina=1/2
a属于(π/2,π) ∴sina=1/2
a=150°
tana=-√3/3

Answer 4

cos2a=1-2sin^2a, sina=1-2sin^2a
2sin^2a+sina-1=0, (2sina-1)(sina+1)=0 , sina=1/2或-1
a属于(π/2,π)，sina=-1(舍去) , sina=1/2 ,a=5π/6
tana=-√3/3

Answer 5

因为sina=cos2a
所以sina=1-2sin²a
即解2sin²a+sina-1=0方程
所以sina=-1 或sina=1/2

因为a属于(π/2,π) ，所以sina大于0，所以sina=1/2
所以a=5π/6
所以tana=--√3/3

Answer 6

sina=1-2sin^2a
2sin^2a+sina-1=0
sina=1/2or-1(don't use)
a=30du
tana=1/3^1/2