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

The general solution for sin^2(x)cos(x)-cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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

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

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

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

Factor

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

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

Solving each part separately

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

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

sin (x) + 1 = 0 : x = \frac{3 π}{2} + 2 πn

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

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

sin (2 θ) = \frac{3}{2}, 0 \leq θ \leq 2 π

- 6 sin^{2} (x) = cos (2 x) - 2

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

- 4 cos (2 θ) - 19 = - 26 cos (θ)

x, z = e^{y} - 3 sin (x y)

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