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

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

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

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

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

Solution steps

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

Subtract

sin^{2} (x)

from both sides

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

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

cos (x) - sin (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{17}{8}

3 csc (θ) = 2

4 sin (x) + 8 = 8

2 cos^{2} (t) - 8 sin^{2} (t) cos (t) - 1 = 0

sin (B) = \frac{4}{5}

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