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

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

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

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

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

Solution steps

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

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

cos (x) tan^{2} (x) = 3 cos (x)

cos (x) = 0.52

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

- 9 tan^{2} (θ) - 1 = - 6 tan (θ)

2 cos (2 θ) - 1 = 0

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