SOLUTION: find solutions of sqrt(3)cos(x)+sin(x)=1, on the interval[0,2pi)

Question 594181: find solutions of sqrt(3)cos(x)+sin(x)=1, on the interval[0,2pi)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find solutions of sqrt(3)cos(x)+sin(x)=1, on the interval[0,2pi
√3cos+sin=1
√3cos=1-sin
square both sides
3cos^2=1-2sin+sin^2
3cos^2=1-2sin+1-cos^2
4cos^2=2-2sin
divide by 2
2cos^2=1-sin
2(1-sin^2)=1-sin
2-2sin^2=1-sin
2sin^2-sin-1=0
(2sinx+1)(sinx-1)
..
2sinx+1=0
sinx=-1/2
x=11π/6
or
sinx-1=0
sinx=1
x=π/2
..
Check:
For x=11π/6
√3cosx+sinx=√3*√3/2-1/2=3/2-1/2=1
..
for x=π/2
√3cosx+sinx=0+1=1

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