# Solve for x sin(x)-tan(x)=0

Rewrite in terms of sines and cosines.
Subtract from both sides of the equation.
Solve for .
Multiply each term by and simplify.
Multiply each term in by .
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Rewrite the equation as .
Divide each term by and simplify.
Divide each term in by .
Simplify .
Dividing two negative values results in a positive value.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Dividing two negative values results in a positive value.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
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 radians in both directions.
, for any integer
Consolidate the answers.
, for any integer
Solve for x sin(x)-tan(x)=0

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