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

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

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

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

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

Solution steps

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

Subtract

2 csc (2 x)

from both sides

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

Factor

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

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

Solving each part separately

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

csc (2 x) = 0 :

No Solution

sec (2 x) - 2 = 0 : x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Combine all the solutions

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

3 cos (x) tan (x) = - 10 tan (x)

sin (x) cos (x) + cos (x) = 0

4 cos^{2} (θ) = 2

2 cos (2 θ) + 3 = 0

3 sin (x) + sin (2 x) = 0

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