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

The general solution for sqrt(2)csc(x)=2 is x= pi/4+2pin,x=(3pi)/4+2pin

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sqrt(2)csc(x)=2

2 csc (x) = 2

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

Solution steps

2 csc (x) = 2

Divide both sides by

2

csc (x) = 2

General solutions for

csc (x) = 2

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

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

cos (x + π) = sin (x)

2 cos^{2} (θ) tan (θ) - tan (θ) = 0

3 - 3 sin (x) - 2 cos^{2} (x) = 0

7 cos^{2} (θ) + 11 cos (θ) = cos (θ) - 3

What is the general solution for sqrt(2)csc(x)=2 ?
The general solution for sqrt(2)csc(x)=2 is x= pi/4+2pin,x=(3pi)/4+2pin