# Solve for x cos(two x) equals ( square root of two) First, divide two

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

The exact value of is .

Divide each term in by .

The common factor should be canceled of .

Cancel the common factor.

Divide by .

First, multiply .

Multiply and .

Multiply by .

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.

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 .

Add.

Multiply by .

Add numerators over the common denominator.

Multiply by .

Subtract from .

Divide each term by and simplify.

Divide each term in by .

The common factor should be canceled.

Cancel the common factor.

Divide by .

Multiply .

Multiply and .

Multiply by .

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 .

Cancel the common factor of .

Cancel the common factor.

Divide by .

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

, for any integer

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