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

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

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

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

x = \frac{π}{2} + 2 πn

Solution steps

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

Subtract

2 csc (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

csc (x) = 1

csc (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn

3 sin (x) + cos (x) = 2

15 cos^{2} (x) - 4 cos (x) - 3 = 0

- 3 sin^{2} (θ) + 3 = - cos (θ) + 2

tan^{2} (x) - 4 sec (x) + 5 = 0

cot (θ) = \frac{3}{4}

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