It is given that tanx=(1+cosx)/2sinx.
a)Show that 3cos^2x+cosx-2=0.
b)Hence,solve tanx=(1+cosx)/2sinx for 0°<=x<=360°.
(Given your answers correct to 1 decimal place if necessary.)
It is given that...
2009-06-11 3:20 am
回答 (1)
2009-06-11 3:38 am
✔ 最佳答案
a)tanx=(1+cosx)/2sinx
sinx/cosx=(1+cosx)/2sinx
2sin2x=cosx(1+cosx)
2(1-cos2x)= cosx+cos2x
2-2cos2x= cosx+cos2x
3cos2x+cosx-2=0
b)
tanx=(1+cosx)/2sinx
3cos2x+cosx-2=0
(3cosx-2)(cosx+1)=0
cosx=2/3 or cosx=-1
x=48.2 o,180o or 311.8 o
收錄日期: 2021-04-23 20:41:58
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