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

The general solution for tan(x)sin(x)+sin(x)=0 is x=2pin,x=pi+2pin,x=(3pi)/4+pin

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tan(x)sin(x)+sin(x)=0

tan (x) sin (x) + sin (x) = 0

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{4} + πn

Solution steps

tan (x) sin (x) + sin (x) = 0

Factor

tan (x) sin (x) + sin (x) : sin (x) (tan (x) + 1)

sin (x) (tan (x) + 1) = 0

Solving each part separately

sin (x) = 0 or tan (x) + 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

tan (x) + 1 = 0 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{4} + πn

2 sin (\frac{x}{5}) + 3 = 0

sin (\frac{θ}{2}) = 1

x, z = arctan (\frac{y}{x})

4 sin^{2} (x) = 2 cos (x) + 1

sin^{2} (x) = 2 + 2 cos (x)

What is the general solution for tan(x)sin(x)+sin(x)=0 ?
The general solution for tan(x)sin(x)+sin(x)=0 is x=2pin,x=pi+2pin,x=(3pi)/4+pin