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

The general solution for 2sin(θ)=csc(θ) is θ= pi/4+2pin,θ=(3pi)/4+2pin,θ=(5pi)/4+2pin,θ=(7pi)/4+2pin

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2sin(θ)=csc(θ)

2 sin (θ) = csc (θ)

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

Solution steps

2 sin (θ) = csc (θ)

Subtract

csc (θ)

from both sides

2 sin (θ) - csc (θ) = 0

Rewrite using trig identities

- csc (θ) + \frac{2}{csc ( θ )} = 0

Solve by substitution

csc (θ) = 2, csc (θ) = - 2

csc (θ) = 2 : θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

csc (θ) = - 2 : θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

Combine all the solutions

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

cos (θ) = - 0.7

2 cos^{2} (x) + 7 cos (x) + 5 = 0

2 sin (x) = - 1, 0 \leq x < 2 π

2 cos^{2} (x) = 3 - 3 sin (x)

sec (3 x) - 4 = 0

What is the general solution for 2sin(θ)=csc(θ) ?
The general solution for 2sin(θ)=csc(θ) is θ= pi/4+2pin,θ=(3pi)/4+2pin,θ=(5pi)/4+2pin,θ=(7pi)/4+2pin