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

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

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

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

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

Solution steps

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

Subtract

sin^{2} (x)

from both sides

1 + cot^{2} (x) - 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

x, 2 cos (x) = 2 cos (3 x)

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

2 sin^{2} (t) - cos (t) - 1 = 0

4 cos^{2} (θ) = 1, 0 \leq θ < 2 π

cos (\frac{x}{2} + \frac{π}{3}) = \frac{2}{2}

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