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

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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

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^{2} (x) + 1)

sin (x) (tan^{2} (x) + 1) = 0

Solving each part separately

sin (x) = 0 or tan^{2} (x) + 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

tan^{2} (x) + 1 = 0 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

cos (4 x) = sin (x), 0 \leq x \leq 2 π

2 cos (x) = 1

sin (θ) = \frac{- 3}{2}

2 cos (\frac{x}{5}) - 2 = 0

2 sin^{2} (x) + 3 = 7 sin (x)

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