What is the general solution for 6sec(x)csc(x)=12csc(x) ?

The general solution for 6sec(x)csc(x)=12csc(x) is x= pi/3+2pin,x=(5pi)/3+2pin

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6sec(x)csc(x)=12csc(x)

6 sec (x) csc (x) = 12 csc (x)

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

6 sec (x) csc (x) = 12 csc (x)

Subtract

12 csc (x)

from both sides

6 sec (x) csc (x) - 12 csc (x) = 0

Factor

6 sec (x) csc (x) - 12 csc (x) : 6 csc (x) (sec (x) - 2)

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

Solving each part separately

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

csc (x) = 0 :

No Solution

sec (x) - 2 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 tan^{2} (θ) + 3 tan (θ) = 0

tan (x) + cot (x) = 2

4 cos^{2} (x) - 4 sin (x) - 5 = 0

x, tan (x^{2} + y^{2}) = 1

2 tan (x) + sec (x) = 0

What is the general solution for 6sec(x)csc(x)=12csc(x) ?
The general solution for 6sec(x)csc(x)=12csc(x) is x= pi/3+2pin,x=(5pi)/3+2pin