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

The general solution for tan^2(θ)sin(θ)=tan^2(θ) is θ=pin

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tan^2(θ)sin(θ)=tan^2(θ)

tan^{2} (θ) sin (θ) = tan^{2} (θ)

θ = πn

Solution steps

tan^{2} (θ) sin (θ) = tan^{2} (θ)

Subtract

tan^{2} (θ)

from both sides

tan^{2} (θ) sin (θ) - tan^{2} (θ) = 0

Factor

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

tan^{2} (θ) (sin (θ) - 1) = 0

Solving each part separately

tan^{2} (θ) = 0 or sin (θ) - 1 = 0

tan^{2} (θ) = 0 : θ = πn

sin (θ) - 1 = 0 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

θ = πn, θ = \frac{π}{2} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn

θ = πn

cos (x) = \frac{1}{cot ( x )}

(sin (x) - 1) \cdot (sin (x) - 3) = 0

2 - 3 cos (θ) = 0

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

tan (θ) = - \frac{3}{4}, sec (θ)

What is the general solution for tan^2(θ)sin(θ)=tan^2(θ) ?
The general solution for tan^2(θ)sin(θ)=tan^2(θ) is θ=pin