# Solve for x in Degrees 2sin(x)^2-cos(x)^2=2

Solve for x in Degrees 2sin(x)^2-cos(x)^2=2
Subtract from both sides of the equation.
Simplify .
Move .
Reorder and .
Factor out of .
Factor out of .
Factor out of .
Apply pythagorean identity.
Subtract from .
Solve for .
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Divide by .
Take the square root of both sides of the equation to eliminate the exponent on the left side.
Simplify .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Plus or minus is .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Simplify the right side.
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.
Subtract from .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
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 degrees in both directions.
, for any integer
, for any integer