What is the general solution for 2sin^2(x)-7sin(x)=-3 ?

The general solution for 2sin^2(x)-7sin(x)=-3 is x= pi/6+2pin,x=(5pi)/6+2pin

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2sin^2(x)-7sin(x)=-3

2 sin^{2} (x) - 7 sin (x) = - 3

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

2 sin^{2} (x) - 7 sin (x) = - 3

Solve by substitution

sin (x) = 3, sin (x) = \frac{1}{2}

sin (x) = 3 :

No Solution

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (\frac{x}{2}) + sin (\frac{x}{2}) = sin (x)

cos (x) + 2 sin^{2} (x) = 1

15 cos (x) - 5 = 4 cos (x)

sin (θ) + cos (θ) = \frac{2 + 3}{2}

x, arctan (\frac{1}{x}) = 8 0^{\circ}

What is the general solution for 2sin^2(x)-7sin(x)=-3 ?
The general solution for 2sin^2(x)-7sin(x)=-3 is x= pi/6+2pin,x=(5pi)/6+2pin