What is the general solution for tan(y)sin^2(y)=3tan(y) ?

The general solution for tan(y)sin^2(y)=3tan(y) is y=pin

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tan(y)sin^2(y)=3tan(y)

tan (y) sin^{2} (y) = 3 tan (y)

y = πn

Solution steps

tan (y) sin^{2} (y) = 3 tan (y)

Subtract

3 tan (y)

from both sides

sin^{2} (y) tan (y) - 3 tan (y) = 0

Factor

sin^{2} (y) tan (y) - 3 tan (y) : tan (y) (sin (y) + 3) (sin (y) - 3)

tan (y) (sin (y) + 3) (sin (y) - 3) = 0

Solving each part separately

tan (y) = 0 or sin (y) + 3 = 0 or sin (y) - 3 = 0

tan (y) = 0 : y = πn

sin (y) + 3 = 0 :

No Solution

sin (y) - 3 = 0 :

No Solution

Combine all the solutions

y = πn

4 cos (x) - 8 sin (x) cos (x) = 0

sin (x) + cos (x) = a

sin (x) = - \frac{1}{2}

tan (x) - \frac{3}{3} = 0

tan (2 θ) = 0.5714

What is the general solution for tan(y)sin^2(y)=3tan(y) ?
The general solution for tan(y)sin^2(y)=3tan(y) is y=pin