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

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

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

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

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

Solution steps

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

Subtract

cos (x)

from both sides

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

tan (x) + 3 cot (x) = 5 sec (x)

6 sin (θ) + 3 = 0

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

sin (3 θ) = - \frac{1}{2}

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