SOLUTION: find all the solution of the equation in the interval (0,2pi) tan(x+pi)+2 sin(x+pi)=0

Question 615760: find all the solution of the equation in the interval (0,2pi)
tan(x+pi)+2 sin(x+pi)=0
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find all the solution of the equation in the interval (0,2pi)
tan(x+pi)+2 sin(x+pi)=0
tan(x+π)/sin(x+π)=-2
[sin(x+π)/cos(x+π)]/sin(x+π)=-2
sin(x+π) cancels out
1/cos(x+π)=-2
cos(x+π)=-1/2
x+π=2π/3 and 4π/3 (in quadrants II and III where cos<0)
x+π=2π/3
x=2π/3-π=-π/3
and
x+π=4π/3
x=4π/3-π=π/3
ans:
x=-π/3 and π/3

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