What is the general solution for csc^2(2x)-cot(2x)=1 ?

The general solution for csc^2(2x)-cot(2x)=1 is x= pi/8+(pin)/2 ,x= pi/4+(pin)/2

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csc^2(2x)-cot(2x)=1

csc^{2} (2 x) - cot (2 x) = 1

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{π}{4} + \frac{πn}{2}

Solution steps

csc^{2} (2 x) - cot (2 x) = 1

Subtract

1

from both sides

csc^{2} (2 x) - cot (2 x) - 1 = 0

Rewrite using trig identities

- cot (2 x) + cot^{2} (2 x) = 0

Solve by substitution

cot (2 x) = 1, cot (2 x) = 0

cot (2 x) = 1 : x = \frac{π}{8} + \frac{πn}{2}

cot (2 x) = 0 : x = \frac{π}{4} + \frac{πn}{2}

Combine all the solutions

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{π}{4} + \frac{πn}{2}

100 tan (x) - 8 = 50 tan (x)

cos (θ) + sin (θ) = 1

2 cos (3 x) = - 1

6 sin (\frac{θ}{2}) = - 6 cos (\frac{θ}{2})

csc (θ) = - \frac{4}{3}

What is the general solution for csc^2(2x)-cot(2x)=1 ?
The general solution for csc^2(2x)-cot(2x)=1 is x= pi/8+(pin)/2 ,x= pi/4+(pin)/2