What is the general solution for 2csc^2(x)-4=0 ?

The general solution for 2csc^2(x)-4=0 is x= pi/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin,x=(7pi)/4+2pin

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2csc^2(x)-4=0

2 csc^{2} (x) - 4 = 0

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Solution steps

2 csc^{2} (x) - 4 = 0

Solve by substitution

csc (x) = 2, csc (x) = - 2

csc (x) = 2 : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

csc (x) = - 2 : x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combine all the solutions

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

2 sin^{2} (θ) - 3 sin (θ) - 2 = 0, 0 \leq θ \leq 2 π

3 sin (2 θ) = 2 cos (2 θ), 0^{\circ} \leq 2 θ < 72 0^{\circ}

csc (x) + 2 = 0

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

sin (x) = - \frac{3}{13}

What is the general solution for 2csc^2(x)-4=0 ?
The general solution for 2csc^2(x)-4=0 is x= pi/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin,x=(7pi)/4+2pin