What is the general solution for 9csc^2(x)+7=19 ?

The general solution for 9csc^2(x)+7=19 is x= pi/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=(5pi)/3+2pin

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9csc^2(x)+7=19

9 csc^{2} (x) + 7 = 19

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

9 csc^{2} (x) + 7 = 19

Solve by substitution

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

csc (x) = - \frac{2 3}{3} : x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sin^{2} (x) = \frac{1}{2} + \frac{1}{2} cos (2 x)

tan (x) = \frac{8}{12}

tan (x) = \frac{8}{10}

3 cot (x) - 1 = 0

4 sin (3 θ) = 0

What is the general solution for 9csc^2(x)+7=19 ?
The general solution for 9csc^2(x)+7=19 is x= pi/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=(5pi)/3+2pin