Question

已知2Sinx=1+Cosx,求角x的大小及其正切

Answer 1

2Sinx=1+Cosx

4sin(x/2)cos(x/2)=2cos²(x/2)

2sin(x/2)=cos(x/2)

即tan(x/2)=sin(x/2)/cos(x/2)=1/2

∴x/2=arctan(1/2)

即x=2arctan(1/2)

tanx=tan(x/2+x/2)

=[tan(x/2)+tan(x/2)]/[1-tan²(x/2)]

=(1/2+1/2)/[1-(1/2)²]

=4/3

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