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

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

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csc(θ/2)=sin(θ/2)

csc (\frac{θ}{2}) = sin (\frac{θ}{2})

θ = π + 4 πn, θ = 3 π + 4 πn

Solution steps

csc (\frac{θ}{2}) = sin (\frac{θ}{2})

Subtract

sin (\frac{θ}{2})

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

csc (\frac{θ}{2}) = 1 : θ = π + 4 πn

csc (\frac{θ}{2}) = - 1 : θ = 3 π + 4 πn

Combine all the solutions

θ = π + 4 πn, θ = 3 π + 4 πn

sin (3 x) = - 1, 0 \leq x \leq 2 π

sin (θ) = 0.25

3 0^{2} = 2 0^{2} + 1 8^{2} - 2 (20) (18) cos (A)

cos (x) = \frac{308}{1475}

tan (θ) = \frac{6}{3}

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