What is the general solution for sin^2(x)cos(x)+sin(x)=0 ?

The general solution for sin^2(x)cos(x)+sin(x)=0 is x=2pin,x=pi+2pin

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sin^2(x)cos(x)+sin(x)=0

sin^{2} (x) cos (x) + sin (x) = 0

x = 2 πn, x = π + 2 πn

Solution steps

sin^{2} (x) cos (x) + sin (x) = 0

Factor

sin^{2} (x) cos (x) + sin (x) : sin (x) (sin (x) cos (x) + 1)

sin (x) (sin (x) cos (x) + 1) = 0

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) cos (x) + 1 = 0 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

x, 8 sec (x) + 8 tan (x) = 8

3 sin (2 x) = 5 cos^{2} (2 x)

x, y^{n} + 25 y = cos (5 x)

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

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

What is the general solution for sin^2(x)cos(x)+sin(x)=0 ?
The general solution for sin^2(x)cos(x)+sin(x)=0 is x=2pin,x=pi+2pin