What is the general solution for sqrt(3)sec(x)csc(x)=2csc(x) ?

The general solution for sqrt(3)sec(x)csc(x)=2csc(x) is x= pi/6+2pin,x=(11pi)/6+2pin

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sqrt(3)sec(x)csc(x)=2csc(x)

3 sec (x) csc (x) = 2 csc (x)

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

Solution steps

3 sec (x) csc (x) = 2 csc (x)

Subtract

2 csc (x)

from both sides

3 sec (x) csc (x) - 2 csc (x) = 0

Factor

3 sec (x) csc (x) - 2 csc (x) : csc (x) (3 sec (x) - 2)

csc (x) (3 sec (x) - 2) = 0

Solving each part separately

csc (x) = 0 or 3 sec (x) - 2 = 0

csc (x) = 0 :

No Solution

3 sec (x) - 2 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

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

(2 sin (x) - 1) (2 cos (x) - 3) = 0

cos (θ) = - \frac{6}{7}

sec (θ) = - 5

sin^{3} (x) = \frac{1}{2}

sin (2 x) - 3 cos (x) = 0

What is the general solution for sqrt(3)sec(x)csc(x)=2csc(x) ?
The general solution for sqrt(3)sec(x)csc(x)=2csc(x) is x= pi/6+2pin,x=(11pi)/6+2pin