What is the general solution for 2sin(θ)-csc(θ)=1 ?

The general solution for 2sin(θ)-csc(θ)=1 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin,θ= pi/2+2pin

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2sin(θ)-csc(θ)=1

2 sin (θ) - csc (θ) = 1

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn, θ = \frac{π}{2} + 2 πn

Solution steps

2 sin (θ) - csc (θ) = 1

Subtract

1

from both sides

2 sin (θ) - csc (θ) - 1 = 0

Rewrite using trig identities

- 1 - csc (θ) + \frac{2}{csc ( θ )} = 0

Solve by substitution

csc (θ) = - 2, csc (θ) = 1

csc (θ) = - 2 : θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

csc (θ) = 1 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn, θ = \frac{π}{2} + 2 πn

\frac{sin ( 2 x )}{4 sin ( 2 x ) - 1} = 1

arctan (x) = 119.74

2 cos (θ) sin (θ) = sin (θ)

4 cos (x) = sec (x)

9.6 = 11.6 cos (3.922 t)

What is the general solution for 2sin(θ)-csc(θ)=1 ?
The general solution for 2sin(θ)-csc(θ)=1 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin,θ= pi/2+2pin