What is the general solution for 2sin^2(a)=-sin(a) ?

The general solution for 2sin^2(a)=-sin(a) is a=2pin,a=pi+2pin,a=(7pi)/6+2pin,a=(11pi)/6+2pin

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2sin^2(a)=-sin(a)

2 sin^{2} (a) = - sin (a)

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

Solution steps

2 sin^{2} (a) = - sin (a)

Solve by substitution

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

sin (a) = 0 : a = 2 πn, a = π + 2 πn

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

Combine all the solutions

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

sec (θ) = 5

tan (w) - 3 tan (w) = 0

tan (φ) = - \frac{1}{2}

cos (θ) = \frac{1}{10}

2 = 2 sin (x)

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