SOLUTION: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.) tan(θ/2) − sin(θ) = 0

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Question 1009490: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)
tan(θ/2) − sin(θ) = 0
Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!
.
Solve - = .
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The half-argument formula says that  = . 

(See, for example, the lesson Trigonometric functions of half argument in this site).


Substitute it into the original equation, and you will get

 -  = .

Now factor it:

. = .

Thus you get two equations:

1)  = ,  which has two solutions   =  and  in the given interval for .


2)  = ,  or   = 0,  which has two solutions   =  and  in the given interval for .

Answer. The solutions are  = , ,  and .


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