What is the general solution for 4sin^2(x)-4sin(x)=-1 ?

The general solution for 4sin^2(x)-4sin(x)=-1 is x= pi/6+2pin,x=(5pi)/6+2pin

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4sin^2(x)-4sin(x)=-1

4 sin^{2} (x) - 4 sin (x) = - 1

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

Solution steps

4 sin^{2} (x) - 4 sin (x) = - 1

Solve by substitution

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

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^{2} (θ) = 3 cos^{2} (θ)

20 sin^{2} (x) + 27 cos (x) = 6

cos^{2} (x) = cos^{2} (x) - sin^{2} (x)

arctan (x) = \frac{2.73}{7.5}

y, sin (x) + cos (y) = ln (x)

What is the general solution for 4sin^2(x)-4sin(x)=-1 ?
The general solution for 4sin^2(x)-4sin(x)=-1 is x= pi/6+2pin,x=(5pi)/6+2pin