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

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

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2sin^2(A)+sin(A)=0

2 sin^{2} (A) + sin (A) = 0

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) = 0

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

3 sin^{2} (x) - 2 sin (x) - 5 = 0

- 2 cos (x) + 4 cos (2 x) = 0

2 tan^{2} (x) - 9 tan (x) + 7 = 0

\frac{1}{2} = cos^{2} (x)

cos (A) = \frac{1}{2}

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