,

Factor out of .

Factor out of .

Factor out of .

Divide each term in by .

Cancel the common factor.

Divide by .

Divide by .

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Set the first factor equal to .

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

The exact value of is .

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

Simplify .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

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

Set the next factor equal to .

Add to both sides of the equation.

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

The exact value of is .

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.

Simplify .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Move to the left of .

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

Plug in for and simplify to see if the solution is contained in .

Plug in for .

Simplify.

Multiply by .

Add and .

The interval contains .

Plug in for and simplify to see if the solution is contained in .

Plug in for .

Simplify.

Multiply by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Move to the left of .

Add and .

The interval contains .

Solve over the Interval sin(2x)-2cos(x)=0 , (0,2pi)