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

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

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tan(x)+sin(x)=0

tan (x) + sin (x) = 0

x = 2 πn, x = π + 2 πn

Solution steps

tan (x) + sin (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 = π + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

cos (x) (2 sin (x) + 1) = 0, 0 \leq x \leq 2 π

3 sin (x) - 1 = 2

sin (t) = \frac{1}{2}

- 2 sin^{2} (θ) + 5 sin (θ) = 2

cot^{2} (x) - 2 cot (x) + 1 = 0

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