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

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

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tan^2(x)sin(x)=sin(x)

tan^{2} (x) sin (x) = sin (x)

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

Solution steps

tan^{2} (x) sin (x) = sin (x)

Subtract

sin (x)

from both sides

tan^{2} (x) sin (x) - sin (x) = 0

Factor

tan^{2} (x) sin (x) - sin (x) : sin (x) (tan (x) + 1) (tan (x) - 1)

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

Solving each part separately

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

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

Combine all the solutions

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

2 sin (2 x) - 3 = 0

2 sin (x) cos (x) = 0

tan^{5} (x) - 9 tan (x) = 0

1 - cos (θ) = \frac{1}{2}

(tan (θ) - 1) (cos (θ) + 1) = 0

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