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

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

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2cot(x)csc(x)-csc^2(x)=0

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

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

Solution steps

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

Factor

2 cot (x) csc (x) - csc^{2} (x) : csc (x) (2 cot (x) - csc (x))

csc (x) (2 cot (x) - csc (x)) = 0

Solving each part separately

csc (x) = 0 or 2 cot (x) - csc (x) = 0

csc (x) = 0 :

No Solution

2 cot (x) - csc (x) = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

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

8 tan (a) + 3 = 2 tan (a) + 3

tan (\frac{θ}{2}) = \frac{3}{3}

x, cos (x) + 1 = 0

- 8 sin (x) = 0

sin (θ + \frac{π}{4}) = 0

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