What is the general solution for 2sin(θ)-3=-csc(θ) ?

The general solution for 2sin(θ)-3=-csc(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin,θ= pi/2+2pin

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2sin(θ)-3=-csc(θ)

2 sin (θ) - 3 = - csc (θ)

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

Solution steps

2 sin (θ) - 3 = - csc (θ)

Subtract

- csc (θ)

from both sides

2 sin (θ) - 3 + csc (θ) = 0

Rewrite using trig identities

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

Solve by substitution

csc (θ) = 2, csc (θ) = 1

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

csc (θ) = 1 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

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

cot (θ) = - 3

2 cos^{2} (t) + 3 cos (t) = - 1

x, cos (x - y) = 1

x, cos (x - y) = 0

sin (a) + 1 = 2 1 - sin^{2} (a)

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