What is the general solution for tan(θ/2)=csc^2(θ)-cot^2(θ) ?

The general solution for tan(θ/2)=csc^2(θ)-cot^2(θ) is θ= pi/2+2pin

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tan(θ/2)=csc^2(θ)-cot^2(θ)

tan (\frac{θ}{2}) = csc^{2} (θ) - cot^{2} (θ)

θ = \frac{π}{2} + 2 πn

Solution steps

tan (\frac{θ}{2}) = csc^{2} (θ) - cot^{2} (θ)

Subtract

csc^{2} (θ) - cot^{2} (θ)

from both sides

tan (\frac{θ}{2}) - csc^{2} (θ) + cot^{2} (θ) = 0

Rewrite using trig identities

tan (\frac{θ}{2}) - 1 = 0

Move

1

to the right side

tan (\frac{θ}{2}) = 1

General solutions for

tan (\frac{θ}{2}) = 1

\frac{θ}{2} = \frac{π}{4} + πn

Solve

\frac{θ}{2} = \frac{π}{4} + πn : θ = \frac{π}{2} + 2 πn

θ = \frac{π}{2} + 2 πn

6 cos^{2} (x) - sin (x) - 4 = 0

cot^{2} (x) = \frac{3}{2} csc (x)

2 cos (θ) - 1 = 0, 0 \leq θ \leq 2 π

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

2 + 3 sin (x) + sin^{2} (x) - cos^{2} (x) = 0

What is the general solution for tan(θ/2)=csc^2(θ)-cot^2(θ) ?
The general solution for tan(θ/2)=csc^2(θ)-cot^2(θ) is θ= pi/2+2pin