# Solve for x cos(x)+1=sin(x) Subtract from both sides of the equation.
Square both sides of the equation.
Remove parentheses.
Move to the left side of the equation by subtracting it from both sides.
Simplify the left side.
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Simplify each term.
Apply the distributive property.
Multiply by .
Expand by multiplying each term in the first expression by each term in the second expression.
Simplify terms.
Combine the opposite terms in .
Reorder the factors in the terms and .
Reorder the factors in the terms and .
Subtract from .
Simplify each term.
Multiply .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite using the commutative property of multiplication.
Multiply .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
Multiply .
Multiply by .
Multiply by .
Multiply by .
Simplify with factoring out.
Move .
Reorder and .
Rewrite as .
Factor out of .
Factor out of .
Rewrite as .
Apply pythagorean identity.
Simplify by adding terms.
Subtract from .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Set the first factor equal to .
Take the inverse sine of both sides of the equation to extract from inside the sine.
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.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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
Set the next factor equal to and solve.
Set the next factor equal to .
Subtract from both sides of the equation.
Multiply each term in by
Multiply each term in by .
Multiply .
Multiply by .
Multiply by .
Multiply by .
Take the inverse sine of both sides of the equation to extract from inside the sine.
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 .
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.
Move to the left of .
Subtract from .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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
The final solution is all the values that make true.
, for any integer
Consolidate and to .
, for any integer
Exclude the solutions that do not make true.
, for any integer
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