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

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

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

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

x = \frac{π}{3} + \frac{2 πn}{3}

Solution steps

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

Solving each part separately

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

cot (\frac{3 x}{2}) = 0 : x = \frac{π}{3} + \frac{2 πn}{3}

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

No Solution

Combine all the solutions

x = \frac{π}{3} + \frac{2 πn}{3}

sec (θ) = \frac{17}{8}

3 sin^{2} (x) = 1

3 sin (θ) + 5 = - 2 sin (θ)

2 - 4 sin (θ) = 0

2 cos (t) = 1, - π \leq t \leq π

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