What is the general solution for 2sin^3(x)+sin^2(x)=0 ?

The general solution for 2sin^3(x)+sin^2(x)=0 is x=2pin,x=pi+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

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2sin^3(x)+sin^2(x)=0

2 sin^{3} (x) + sin^{2} (x) = 0

x = 2 πn, x = π + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

2 sin^{3} (x) + sin^{2} (x) = 0

Solve by substitution

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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

cos (2 x) = cos (4 x)

14 sin^{2} (x) - 7 sin (x) = 0

cos (α) = \frac{2}{3}

sec (- 2 x) = - 2

What is the general solution for 2sin^3(x)+sin^2(x)=0 ?
The general solution for 2sin^3(x)+sin^2(x)=0 is x=2pin,x=pi+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin