Solve for x sin(x)^2-sin(x)=0

Problem

sin(x)−sin(x)=0

Solution

1. Factor the common term sin(x) from the expression.

sin(x)*(sin(x)−1)=0

2. Apply the zero product property to set each factor equal to zero.

sin(x)=0

sin(x)−1=0⇒sin(x)=1

3. Solve for x in the first equation sin(x)=0 by identifying where the sine function is zero on the unit circle.

x=n*π

4. Solve for x in the second equation sin(x)=1 by identifying where the sine function is one on the unit circle.

x=π/2+2*n*π

5. Combine the solutions, where n represents any integer.

x=n*π,π/2+2*n*π

Final Answer

sin(x)−sin(x)=0⇒x=n*π,π/2+2*n*π

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