What is the general solution for 2sin(v)csc(v)-csc(v)=4sin(v)-2 ?

The general solution for 2sin(v)csc(v)-csc(v)=4sin(v)-2 is v= pi/6+2pin,v=(5pi)/6+2pin

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2sin(v)csc(v)-csc(v)=4sin(v)-2

2 sin (v) csc (v) - csc (v) = 4 sin (v) - 2

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

Solution steps

2 sin (v) csc (v) - csc (v) = 4 sin (v) - 2

Subtract

4 sin (v) - 2

from both sides

2 sin (v) csc (v) - csc (v) - 4 sin (v) + 2 = 0

Factor

2 sin (v) csc (v) - csc (v) - 4 sin (v) + 2 : (2 sin (v) - 1) (csc (v) - 2)

(2 sin (v) - 1) (csc (v) - 2) = 0

Solving each part separately

2 sin (v) - 1 = 0 or csc (v) - 2 = 0

2 sin (v) - 1 = 0 : v = \frac{π}{6} + 2 πn, v = \frac{5 π}{6} + 2 πn

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

Combine all the solutions

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

2 cos (2 x) = 4 cos (x)

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sin (θ) = \frac{16}{14}

tan (θ) = \frac{83}{47}

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

What is the general solution for 2sin(v)csc(v)-csc(v)=4sin(v)-2 ?
The general solution for 2sin(v)csc(v)-csc(v)=4sin(v)-2 is v= pi/6+2pin,v=(5pi)/6+2pin