# Solve for x in Radians cos(x)^2+sin(x)=1

Solve for x in Radians cos(x)^2+sin(x)=1
Subtract from both sides of the equation.
Simplify .
Move .
Reorder and .
Rewrite as .
Factor out of .
Factor out of .
Rewrite as .
Apply pythagorean identity.
Solve for .
Factor the left side of the equation.
Let . Substitute for all occurrences of .
Factor out of .
Factor out of .
Raise to the power of .
Factor out of .
Factor out of .
Replace all occurrences of with .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
Set equal to .
Solve for .
Take the inverse sine of both sides of the equation to extract from inside the sine.
Simplify the right side.
The exact value of is .
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second 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 radians in both directions.
, for any integer
, for any integer
, for any integer
Set equal to and solve for .
Set equal to .
Solve for .
Subtract from both sides of the equation.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Dividing two negative values results in a positive value.
Divide by .
Simplify the right side.
Divide by .
Take the inverse sine of both sides of the equation to extract from inside the sine.
Simplify the right side.
The exact value of is .
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.
Simplify .
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of .
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 radians in both directions.
, for any integer
, for any integer
, for any integer
The final solution is all the values that make true.
, for any integer
, for any integer
Consolidate and to .
, for any integer
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