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

The general solution for tan(x)sin(x)+2sin(x)=0 is x=2pin,x=pi+2pin,x=-1.10714…+pin

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

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

x = 2 πn, x = π + 2 πn, x = - 1.10714 \dots + πn

Solution steps

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

Factor

tan (x) sin (x) + 2 sin (x) : sin (x) (tan (x) + 2)

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

Solving each part separately

sin (x) = 0 or tan (x) + 2 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

tan (x) + 2 = 0 : x = arctan (- 2) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (- 2) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = - 1.10714 \dots + πn

cos (4 x) - cos (2 x) = 0

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

2 cos (θ) = - 2

tan (\frac{x}{3}) = 3

cos (\frac{x}{2}) - 1 = 0

What is the general solution for tan(x)sin(x)+2sin(x)=0 ?
The general solution for tan(x)sin(x)+2sin(x)=0 is x=2pin,x=pi+2pin,x=-1.10714…+pin