What is the general solution for 4csc^2(x/2)-6csc(x/2)-4=0 ?

The general solution for 4csc^2(x/2)-6csc(x/2)-4=0 is x= pi/3+4pin,x=(5pi)/3+4pin

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4csc^2(x/2)-6csc(x/2)-4=0

4 csc^{2} (\frac{x}{2}) - 6 csc (\frac{x}{2}) - 4 = 0

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

Solution steps

4 csc^{2} (\frac{x}{2}) - 6 csc (\frac{x}{2}) - 4 = 0

Solve by substitution

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

csc (\frac{x}{2}) = 2 : x = \frac{π}{3} + 4 πn, x = \frac{5 π}{3} + 4 πn

csc (\frac{x}{2}) = - \frac{1}{2} :

No Solution

Combine all the solutions

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

2 tan (θ) + sec^{2} (θ) = 4

2 sin^{2} (x) + 2 sin (x) - 1 = 0

csc (x) = 7

2 cos (θ) sin (θ) + cos (θ) - 2 sin (θ) = 1

sin (2 θ) - cos (θ) - 2 sin (θ) + 1 = 0

What is the general solution for 4csc^2(x/2)-6csc(x/2)-4=0 ?
The general solution for 4csc^2(x/2)-6csc(x/2)-4=0 is x= pi/3+4pin,x=(5pi)/3+4pin