Trig. Equation

Solve the equation：
10Sinx(Cosx+1)=7
0 < x < 360 degree
Sol
設 p=Tan(x/2)
Sinx=2p/(1+p^2)
Cosx=(1－p^2)/(1+p^2)
10Sinx(Cosx+1)=7
10*2p/(1+p^2)[(1－p^2)/(1+p^2)+1]=7
20p*(1－p^2+1+p^2)=7(1+p^2)^2
40p=7(p^4+2p^2+1)
7p^4+14p^2-40p+7=0
(p－0.188)(p－1.323)(7p^2+10.566p+28.240807)=0
(p－0.188)(p－1.323)=0
p=0.188 or p=1.323
Tan(x/2)=0.188 or Tan(x/2)=1.323
0 < x < 360 degree
0<x/2<180 degree
x/2=10.65degree or x/w=52.9degree
x=21.3degreeor x=105.8degree

用 sinx = 2t/(1+t²)

cosx = (1-t²)/(1+t²)

2014-01-19 16:56:47 補充：
Sorry! 原來是我計錯數，做唔到。