Solve for x sin(x/2)=1-sin(x/2)

Problem

sin(x/2)=1−sin(x/2)

Solution

1. Isolate the trigonometric term by adding sin(x/2) to both sides of the equation.

2*sin(x/2)=1

2. Divide both sides by 2 to solve for the sine function.

sin(x/2)=1/2

3. Determine the reference angle for which the sine is 1/2 which is π/6 (or 30.

x/2=π/6+2*π*n

x/2=(5*π)/6+2*π*n

4. Solve for x by multiplying both sides of each equation by 2

x=π/3+4*π*n

x=(5*π)/3+4*π*n

Final Answer

sin(x/2)=1−sin(x/2)⇒x=π/3+4*π*n,(5*π)/3+4*π*n

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