What is the general solution for 3csc(x)+5=csc(x)+9 ?

The general solution for 3csc(x)+5=csc(x)+9 is x= pi/6+2pin,x=(5pi)/6+2pin

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3csc(x)+5=csc(x)+9

3 csc (x) + 5 = csc (x) + 9

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

Solution steps

3 csc (x) + 5 = csc (x) + 9

Solve by substitution

csc (x) = 2

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

Combine all the solutions

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

3 = tan^{2} (x)

tan (θ) csc (θ) + 2 tan (θ) = 0

250 = 88 sin (θ) + 242 cos (θ)

4 + 2 csc (\frac{θ}{2}) = 8

2 cos (3 x) = \frac{1}{2}, x = \frac{17 π}{4}

What is the general solution for 3csc(x)+5=csc(x)+9 ?
The general solution for 3csc(x)+5=csc(x)+9 is x= pi/6+2pin,x=(5pi)/6+2pin