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

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

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

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

x = \frac{π}{4} + πn

Solution steps

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

Subtract

csc^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cot (x) = 1

cot (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{π}{4} + πn

2 csc (2 x) cot (2 x) = 0

3 cos (y) + cot (y) = 0

2 sin (x) - 3 sin (x) + 1 = 0

2 sin (x) (sin (x) - 1) = 3 cos^{2} (x)

2 sin^{2} (x) = 2 sin (x) + 4

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