What is the general solution for 3csc(x)=2csc(x)+sqrt(2) ?

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

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3csc(x)=2csc(x)+sqrt(2)

3 csc (x) = 2 csc (x) + 2

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

Solution steps

3 csc (x) = 2 csc (x) + 2

Solve by substitution

csc (x) = 2

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

Combine all the solutions

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

sec (x) = tan (x) + cot (x)

cos (3 x) = - \frac{1}{2} 3

2 sin (2 x) + 3 = 0, 0 \leq x \leq 2 π

x, cos (x) = \frac{1}{3}

cos (θ) = - 0.02

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