What is the general solution for sin(θ)tan^2(θ)-sin(θ)=0 ?

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

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sin(θ)tan^2(θ)-sin(θ)=0

sin (θ) tan^{2} (θ) - sin (θ) = 0

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

Solution steps

sin (θ) tan^{2} (θ) - sin (θ) = 0

Factor

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

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

Solving each part separately

sin (θ) = 0 or tan (θ) + 1 = 0 or tan (θ) - 1 = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

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

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

Combine all the solutions

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

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- 11 cos (x) (22) - 11 sin (x) (8) = - 250

3 cos (x) + 1 = 2 sin (x)

\frac{π}{6} = cos (2 x)

\frac{5}{csc ( x )} - 53 cos (x) = 0

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