# Solve for x two sin(x) minus sin(two x) equals zero

Factor out of .

Factor out of .

Factor out of .

Should be rewritten as .

First, divide each term in by .

Cancel the common factor.

Divide by .

First, divide by .

In case any individual factor in the left part of the equation equals , the entire expression will be equal to .

Set the Initially factor equal to .

Take the inverse sine of both sides of the equation to extract from inside the sine.

The exact value of is .

The 1st and 2nd quadrants of the sine function are positive. To calculate the second answer, subtract the reference angle from to find the solution in the second quadrant.

First, subtract from .

Calculate the period.

Evaluate the period of function using .

Replace with in the formula for period.

Find solution to the equation.

The absolute value is the distance between a number and zero. The distance between and is .

Divide by .

The period of the function is so values will repeat every radians in two directions at once.

, for any integer

, for any integer

Set the Then factor equal to .

Subtract from both sides of the equation.

First, multiply each term in by

Multiply each term in by .

Multiply .

Multiply by .

Multiply by .

Multiply by .

Take the inverse cosine of both sides of the equation to extract from inside the cosine.

The exact value of is .

The 1st and 4th quadrants of the cosine function are positive. To calculate the second answer, subtract the reference angle from to find the solution in the fourth quadrant.

Subtract from .

Find the period.

The period of the function can be calculated using .

Replace with in the formula for period.

Solve the equation.

The absolute value is the distance between a number and zero. The distance between and is .

Divide by .

The period of the function is so values will repeat every radians in both directions.

, for any integer

, for any integer

The final solution is all the values that make true.

, for any integer

Consolidate the answers.

, for any integer

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