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

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

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

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

x = \frac{7 π}{6} + 2 πn, x = \frac{11 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) = \frac{1}{2}, csc (x) = - 2

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

No Solution

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

Combine all the solutions

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

t, f = 2 sin (k t)

cos (\frac{( 2 x - π )}{4}) = 1

\frac{5}{6} sin (10 x - 0.927) = 5

3 sin (t) = 1 + sin (t)

sin^{2} (t) sin (t) = 0

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