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

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

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sin(x)-tan(x)=0

sin (x) - tan (x) = 0

x = 2 πn, x = π + 2 πn

Solution steps

sin (x) - tan (x) = 0

Express with sin, cos

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

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

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

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

sin (x + 2 0^{\circ}) = cos (x)

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

1 - sin (x) = cos (x)

cos^{2} (θ) - cos (θ) = 0

cos (θ) = \frac{12}{13}

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