What is the general solution for tan(x)=-3cos(x)tan(x) ?

The general solution for tan(x)=-3cos(x)tan(x) is x=pin,x=1.91063…+2pin,x=-1.91063…+2pin

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tan(x)=-3cos(x)tan(x)

tan (x) = - 3 cos (x) tan (x)

x = πn, x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

Solution steps

tan (x) = - 3 cos (x) tan (x)

Subtract

- 3 cos (x) tan (x)

from both sides

tan (x) + 3 cos (x) tan (x) = 0

Factor

tan (x) + 3 cos (x) tan (x) : tan (x) (3 cos (x) + 1)

tan (x) (3 cos (x) + 1) = 0

Solving each part separately

tan (x) = 0 or 3 cos (x) + 1 = 0

tan (x) = 0 : x = πn

3 cos (x) + 1 = 0 : x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn

Combine all the solutions

x = πn, x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn

Show solutions in decimal form

x = πn, x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

tan (x - \frac{π}{4}) = \frac{1}{6}

csc (2 χ) = \frac{1}{1 - cos ( 2 χ )}

cos (2 x) - 2 sin (x) = 1

3 cos (x) - sin (x) = - 1

x, g = f (sin (6 x - 7 y))

What is the general solution for tan(x)=-3cos(x)tan(x) ?
The general solution for tan(x)=-3cos(x)tan(x) is x=pin,x=1.91063…+2pin,x=-1.91063…+2pin