What is the general solution for 2sin(x)-tan(x)=0 ?

The general solution for 2sin(x)-tan(x)=0 is x=2pin,x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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2sin(x)-tan(x)=0

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

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Express with sin, cos

\frac{- sin ( x ) + 2 cos ( x ) sin ( x )}{cos ( x )} = 0

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

- sin (x) + 2 cos (x) sin (x) = 0

Factor

- sin (x) + 2 cos (x) sin (x) : sin (x) (2 cos (x) - 1)

sin (x) (2 cos (x) - 1) = 0

Solving each part separately

sin (x) = 0 or 2 cos (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 cos (x) - 1 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

(cos (x) + 1) (cos (x) - 4) = 0

cos (10 x) = 0

7 - 5 cos (x) = 10

sin^{2} (θ) - 2 = sin (θ)

5 + 4 cos (x) = 0

What is the general solution for 2sin(x)-tan(x)=0 ?
The general solution for 2sin(x)-tan(x)=0 is x=2pin,x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin