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

The general solution for 4sin^2(x)+1=-4sin(x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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

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

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

Solution steps

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

Solve by substitution

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

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

Combine all the solutions

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

cos (3 x + 6 0^{\circ}) = 0

2 sin^{2} (x) + (- 2 - 2) sin (x) + 2 = 0

3 - 3 tan (2 x) = 4 - 23 tan (2 x)

cos (θ) = \frac{3}{34}

tan (θ) + cot (θ) = \frac{4}{3}

What is the general solution for 4sin^2(x)+1=-4sin(x) ?
The general solution for 4sin^2(x)+1=-4sin(x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin