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

The general solution for 3tan(x)=sin(x) is x=2pin,x=pi+2pin

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3tan(x)=sin(x)

3 tan (x) = sin (x)

x = 2 πn, x = π + 2 πn

Solution steps

3 tan (x) = sin (x)

Subtract

sin (x)

from both sides

3 tan (x) - sin (x) = 0

Express with sin, cos

\frac{3 sin ( x ) - cos ( x ) sin ( x )}{cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

3 sin (x) - cos (x) sin (x) = 0

Factor

3 sin (x) - cos (x) sin (x) : - sin (x) (cos (x) - 3)

- sin (x) (cos (x) - 3) = 0

Solving each part separately

sin (x) = 0 or cos (x) - 3 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

cos (x) - 3 = 0 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

5 = sinh (x)

- 16 cos (2 x) = 0

62 + 12 cos (x - 4 5^{\circ}) = 0

(2 \cdot 9.8 \cdot l (1 - cos (θ))) = 0.018

\frac{1}{tan ( x )} = 0.5

What is the general solution for 3tan(x)=sin(x) ?
The general solution for 3tan(x)=sin(x) is x=2pin,x=pi+2pin