# Solve for x sec(x plus eighty minus one) equals two

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

The exact value of is .

Subtract from both sides of the equation.

The secant function is positive in the Initially and fourth quadrants. To calculate the second answer, subtract the reference angle from to find the solution in the fourth quadrant.

Clarify .

To write as a fraction with a common denominator, First, 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.

Clarify the numerator.

Multiply by .

Subtract from .

Subtract from both sides of the equation.

Add to until the angle falls between and . In such a case, needs to be added times.

Simplify.

First, 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.

Multiply by .

Add and .

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 .

First, 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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