# Solve for x 4cos(x-1)^2=0

Divide each term in by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by .

Divide by .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

Simplify the right side of the equation.

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

is equal to .

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

The exact value of is .

Add to both sides of the equation.

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 .

Add to both sides of the equation.

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

Consolidate the answers.

, for any integer

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