What is the general solution for 4+2csc(θ/2)=8 ?

The general solution for 4+2csc(θ/2)=8 is θ= pi/3+4pin,θ=(5pi)/3+4pin

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4+2csc(θ/2)=8

4 + 2 csc (\frac{θ}{2}) = 8

θ = \frac{π}{3} + 4 πn, θ = \frac{5 π}{3} + 4 πn

Solution steps

4 + 2 csc (\frac{θ}{2}) = 8

Move

4

to the right side

2 csc (\frac{θ}{2}) = 4

Divide both sides by

2

csc (\frac{θ}{2}) = 2

General solutions for

csc (\frac{θ}{2}) = 2

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

Solve

\frac{θ}{2} = \frac{π}{6} + 2 πn : θ = \frac{π}{3} + 4 πn

Solve

\frac{θ}{2} = \frac{5 π}{6} + 2 πn : θ = \frac{5 π}{3} + 4 πn

θ = \frac{π}{3} + 4 πn, θ = \frac{5 π}{3} + 4 πn

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

cos (θ) = sin (3 6^{\circ})

2 sec^{2} (x) = tan^{2} (x) + 2 sec (x) + 4

cos^{2} (θ) + sin (θ) + 1 = 0

cos (x) = \frac{22.5}{34}

What is the general solution for 4+2csc(θ/2)=8 ?
The general solution for 4+2csc(θ/2)=8 is θ= pi/3+4pin,θ=(5pi)/3+4pin