What is the general solution for 12csc(x)=3csc(x)+6sqrt(3) ?

The general solution for 12csc(x)=3csc(x)+6sqrt(3) is x= pi/3+2pin,x=(2pi)/3+2pin

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12csc(x)=3csc(x)+6sqrt(3)

12 csc (x) = 3 csc (x) + 63

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

Solution steps

12 csc (x) = 3 csc (x) + 63

Solve by substitution

csc (x) = \frac{2 3}{3}

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

Combine all the solutions

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

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

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

4 cot (x) + 5 = 1

\frac{1}{36} + cos^{2} (θ) = 1

2 sin (x) - (2 + 2) = - 2 csc (x)

What is the general solution for 12csc(x)=3csc(x)+6sqrt(3) ?
The general solution for 12csc(x)=3csc(x)+6sqrt(3) is x= pi/3+2pin,x=(2pi)/3+2pin