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

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

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sqrt(2)csc^2(x)+csc(x)-sqrt(2)=0

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

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

Solution steps

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

Solve by substitution

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

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

No Solution

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

Combine all the solutions

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

2 sin (A) - 1 = 0

cos (5 θ) = cos (3 θ)

cos (x 1) - cos (x 2) = cos (x 1 - x 2)

8 \cdot sin^{2} (2 x) - 2 \cdot sin (2 x) - 1 = 0

4 - 2 cos (2 x) = 0

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