What is the general solution for 4sin^2(x)=3-4sin(x) ?

The general solution for 4sin^2(x)=3-4sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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4sin^2(x)=3-4sin(x)

4 sin^{2} (x) = 3 - 4 sin (x)

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

Solution steps

4 sin^{2} (x) = 3 - 4 sin (x)

Solve by substitution

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

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

sin (x) = - \frac{3}{2} :

No Solution

Combine all the solutions

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

tan (θ) = - \frac{2}{2}

\frac{sin ( 7 8 ^{\circ} )}{14} = \frac{sin ( a )}{6}

tan (x) = (- \frac{6}{5})

cos (x^{2}) = 1

2 sin^{2} (θ) + cos (θ) - 2 = 0

What is the general solution for 4sin^2(x)=3-4sin(x) ?
The general solution for 4sin^2(x)=3-4sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin