What is the general solution for solvefor θ,2sin(θ)=csc(θ)+1 ?

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

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solvefor θ,2sin(θ)=csc(θ)+1

solve for

θ, 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

csc (θ) + 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

sin^{2} (x) \cdot 2 cos (x) = 2

cos (θ) = \frac{20}{27}

32 cos (x) + 2 = - 1

\frac{1}{sin ( x ) \cdot cos ( x ) + cos ( x )} = \frac{1}{cos ( x )}

4 = tan^{2} (4 5^{\circ} + \frac{x}{2})

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