What is the general solution for 2sin(θ)-3csc(θ)+5=0 ?

The general solution for 2sin(θ)-3csc(θ)+5=0 is θ= pi/6+2pin,θ=(5pi)/6+2pin

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2sin(θ)-3csc(θ)+5=0

2 sin (θ) - 3 csc (θ) + 5 = 0

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

Solution steps

2 sin (θ) - 3 csc (θ) + 5 = 0

Rewrite using trig identities

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

Solve by substitution

csc (θ) = - \frac{1}{3}, csc (θ) = 2

csc (θ) = - \frac{1}{3} :

No Solution

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

Combine all the solutions

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

csc^{4} (2 x) - 4 = 0

sin (θ) = \frac{4}{13}

sin (3 x) = - \frac{1}{2}, 0 \leq x \leq 2 π

4 cos (x) - 3 sec (x) = 0

sin (θ) = \frac{11}{61}

What is the general solution for 2sin(θ)-3csc(θ)+5=0 ?
The general solution for 2sin(θ)-3csc(θ)+5=0 is θ= pi/6+2pin,θ=(5pi)/6+2pin