What is the general solution for 3csc(x)=4+csc(x) ?

The general solution for 3csc(x)=4+csc(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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3csc(x)=4+csc(x)

3 csc (x) = 4 + csc (x)

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

3 csc (x) = 4 + csc (x)

Solve by substitution

csc (x) = 2

csc (x) = 2 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

tan (θ) = - \frac{8}{15}

4 cos (t) = 0

7 sec^{3} (x) + 16 sec^{2} (x) + 11 sec (x) + 2 = 0

1 + sin (5 x) = 0

0 = \frac{π}{2} - 2 arctan (\frac{\frac{π}{2} - 2 - c}{\frac{π}{2} - c})

What is the general solution for 3csc(x)=4+csc(x) ?
The general solution for 3csc(x)=4+csc(x) is x= pi/6+2pin,x=(5pi)/6+2pin