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

The general solution for sin^2(x)+sin(x)cos(x)=0 is x=2pin,x=pi+2pin,x=(3pi)/4+pin

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

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

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{4} + πn

Solution steps

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{3 π}{4} + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{4} + πn

4 sin (x) + 5 = 4 + sin (x)

9 sin (θ) - 1 = 7 sin (θ)

cot (x) = sin (x)

- 3 cos (x) - sin (x) = - 3

9 cot^{2} (x) = 3

What is the general solution for sin^2(x)+sin(x)cos(x)=0 ?
The general solution for sin^2(x)+sin(x)cos(x)=0 is x=2pin,x=pi+2pin,x=(3pi)/4+pin