What is the general solution for cot^2(x)+1=sin^2(x) ?

The general solution for cot^2(x)+1=sin^2(x) is x= pi/2+2pin,x=(3pi)/2+2pin

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cot^2(x)+1=sin^2(x)

cot^{2} (x) + 1 = sin^{2} (x)

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

cot^{2} (x) + 1 = sin^{2} (x)

Subtract

sin^{2} (x)

from both sides

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

Rewrite using trig identities

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

Factor

csc^{2} (x) - sin^{2} (x) : (csc (x) + sin (x)) (csc (x) - sin (x))

(csc (x) + sin (x)) (csc (x) - sin (x)) = 0

Solving each part separately

csc (x) + sin (x) = 0 or csc (x) - sin (x) = 0

csc (x) + sin (x) = 0 :

No Solution

csc (x) - sin (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

(4 + tan (x)) (3 sin (x) - 2) = 0

sec (2 x) - 1 = 0

sin (2 x) + sin (x) + 2 cos (x) + 1 = 0

csc (x) = \frac{13}{5}

6 csc (θ) + 7 = 0

What is the general solution for cot^2(x)+1=sin^2(x) ?
The general solution for cot^2(x)+1=sin^2(x) is x= pi/2+2pin,x=(3pi)/2+2pin