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

The general solution for sin^2(x)=sin(x)cos(x) is x=2pin,x=pi+2pin,x= pi/4+pin

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

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

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn

Solution steps

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

Subtract

sin (x) cos (x)

from both sides

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

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) - cos (x) = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn

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

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

cos^{2} (θ) = 0

cos (7 x) cos (2 x) + sin (7 x) sin (2 x) = \frac{1}{2}

sin (2 x) = \frac{1}{2}, 0 \leq x \leq 2 π

What is the general solution for sin^2(x)=sin(x)cos(x) ?
The general solution for sin^2(x)=sin(x)cos(x) is x=2pin,x=pi+2pin,x= pi/4+pin