What is the general solution for sqrt(3)csc((2x)/3)-2=0 ?

The general solution for sqrt(3)csc((2x)/3)-2=0 is x= pi/2+3pin,x=pi+3pin

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sqrt(3)csc((2x)/3)-2=0

3 csc (\frac{2 x}{3}) - 2 = 0

x = \frac{π}{2} + 3 πn, x = π + 3 πn

Solution steps

3 csc (\frac{2 x}{3}) - 2 = 0

Move

2

to the right side

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

Divide both sides by

3

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

General solutions for

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

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

Solve

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

Solve

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

x = \frac{π}{2} + 3 πn, x = π + 3 πn

cos (θ) = \frac{8}{10}

5 sin (a) + 3 = sin (a) + 2

csc (3 x) = 2

sin (x) = 0, 6

4 cos^{2} (θ) - 3 = 0, 0 \leq θ \leq 2 π

What is the general solution for sqrt(3)csc((2x)/3)-2=0 ?
The general solution for sqrt(3)csc((2x)/3)-2=0 is x= pi/2+3pin,x=pi+3pin