What is the general solution for 4sin^2(x)=3,+[0,+2pi] ?

The general solution for 4sin^2(x)=3,+[0,+2pi] is x= pi/3 ,x=(2pi)/3 ,x=(4pi)/3 ,x=(5pi)/3

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4sin^2(x)=3,+[0,+2pi]

4 sin^{2} (x) = 3, + [0, + 2 π]

x = \frac{π}{3}, x = \frac{2 π}{3}, x = \frac{4 π}{3}, x = \frac{5 π}{3}

Solution steps

4 sin^{2} (x) = 3, [0, + 2 π]

Solve by substitution

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

sin (x) = \frac{3}{2}, [0, + 2 π] : x = \frac{π}{3}, x = \frac{2 π}{3}

sin (x) = - \frac{3}{2}, [0, + 2 π] : x = \frac{4 π}{3}, x = \frac{5 π}{3}

Combine all the solutions

x = \frac{π}{3}, x = \frac{2 π}{3}, x = \frac{4 π}{3}, x = \frac{5 π}{3}

6 sin (θ) - 1 = 4 sin (θ)

cot^{3} (x) = cot^{3} (x) sin (x)

3 (1 - cos (x)) = sin^{2} (x)

2 cos^{2} (θ) + 5 cos (θ) - 2 = - 4

tan (x) = \frac{2}{4}

What is the general solution for 4sin^2(x)=3,+[0,+2pi] ?
The general solution for 4sin^2(x)=3,+[0,+2pi] is x= pi/3 ,x=(2pi)/3 ,x=(4pi)/3 ,x=(5pi)/3