一條中4maths-口-救我/3\急!!!!!!!!!

2008-02-14 7:31 am
[a]:prove that tanx+cotx=2/sin2x

[b]:if y=2+√3 is a root of the equation y^2-(tanx+cotx)y+1\\0,
find the values of sin2x and cos4x.

回答 (1)

2008-02-14 7:54 am
✔ 最佳答案
[a] tanx + cotx
= sinx/cosx + cosx/sinx
= ( (sinx)^2 + (cosx)^2 ) / sinxcosx
= 1/ sinxcosx
= 2/2sinxcosx
= 2/sin2x

[b] y^2 -(tanx+cotx) y+1=0
tanx+cotx= (y^2+1)/y
= (7+4√3 +1) / (2+√3)
= 4

tanx+cotx = 2 / sin2x = 4
sin2x = 1/2
2x = pi/6 + 2*k*pi
4x = pi/3 + 2*k*pi
cos4x = 1/2

2008-02-15 22:43:43 補充:
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收錄日期: 2021-04-23 19:43:46
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