# Solve for x in Degrees 8cos(x)tan(x)=-tan(x)

Solve for x in Degrees 8cos(x)tan(x)=-tan(x)
Rewrite in terms of sines and cosines, then cancel the common factors.
Reorder and .
Rewrite in terms of sines and cosines.
Cancel the common factors.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Separate fractions.
Rewrite in terms of sines and cosines.
Multiply by the reciprocal of the fraction to divide by .
Write as a fraction with denominator .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Simplify the right side.
Dividing two negative values results in a positive value.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
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.
Move the negative in front of the fraction.
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Simplify the right side.
Evaluate .
The cosine function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third 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
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