What is the general solution for 2cot^2(y)+3csc(y)=0 ?

The general solution for 2cot^2(y)+3csc(y)=0 is y=(7pi)/6+2pin,y=(11pi)/6+2pin

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2cot^2(y)+3csc(y)=0

2 cot^{2} (y) + 3 csc (y) = 0

y = \frac{7 π}{6} + 2 πn, y = \frac{11 π}{6} + 2 πn

Solution steps

2 cot^{2} (y) + 3 csc (y) = 0

Rewrite using trig identities

(- 1 + csc^{2} (y)) \cdot 2 + 3 csc (y) = 0

Solve by substitution

csc (y) = \frac{1}{2}, csc (y) = - 2

csc (y) = \frac{1}{2} :

No Solution

csc (y) = - 2 : y = \frac{7 π}{6} + 2 πn, y = \frac{11 π}{6} + 2 πn

Combine all the solutions

y = \frac{7 π}{6} + 2 πn, y = \frac{11 π}{6} + 2 πn

cot (x) = - 0.456

4 tan^{2} (θ) - 2 tan (θ) + 3 = - 7 tan (θ) + 2

- 2 = csc (θ)

2 cot (x) = csc^{2} (x)

2 csc (2 x) cot (2 x) = 0

What is the general solution for 2cot^2(y)+3csc(y)=0 ?
The general solution for 2cot^2(y)+3csc(y)=0 is y=(7pi)/6+2pin,y=(11pi)/6+2pin