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

The general solution for 2cot^2(x)-3csc(x)=0 is x= pi/6+2pin,x=(5pi)/6+2pin

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

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

csc (x) = 2 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

csc (x) = - \frac{1}{2} :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

3 - 4 cos^{2} (x) = 0

sin (2 θ) = - \frac{1}{2}, 0 \leq θ \leq 2 π

sin (\frac{1}{x}) = 0

cos (θ) = \frac{40}{41}

- 3 cos (2 θ) + 3 = 5 sin (θ)

What is the general solution for 2cot^2(x)-3csc(x)=0 ?
The general solution for 2cot^2(x)-3csc(x)=0 is x= pi/6+2pin,x=(5pi)/6+2pin