Apply the sine double–angle identity.

Substitute for .

Raise to the power of .

Factor out of .

Factor out of .

Factor out of .

Rewrite as .

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

Substitute for .

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

The exact value of is .

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.

Multiply by .

Add and .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

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 .

Cancel the common factor of .

Cancel the common factor.

Divide by .

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

, for any integer

Consolidate the answers.

, for any integer

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