What is the general solution for 3cos(x)tan(x)+tan(x)=0 ?

The general solution for 3cos(x)tan(x)+tan(x)=0 is x=pin,x=1.91063…+2pin,x=-1.91063…+2pin

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

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

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

Solution steps

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

Factor

3 cos (x) tan (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

sin (x) = \frac{3}{2}

3 sin (x) = 1 + cos (2 x)

2 cos^{2} (θ) + 3 cos (θ) = 0

5 (sin (θ) + 1) = 5

cos (\frac{x}{2}) = \frac{3}{2}

What is the general solution for 3cos(x)tan(x)+tan(x)=0 ?
The general solution for 3cos(x)tan(x)+tan(x)=0 is x=pin,x=1.91063…+2pin,x=-1.91063…+2pin