# Solve for x sec(x+81)=2

Solve for x sec(x+81)=2
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 first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Simplify the expression to find the second solution.
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 .
Subtract from both sides of the equation.
Add to until the angle falls between and . In this case, needs to be added times.
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.
Multiply by .