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

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

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csc^2(x)=sin(x)

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

x = \frac{π}{2} + 2 πn

Solution steps

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

Subtract

sin (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

csc (x) = 1, csc (x) = - \frac{1}{2} + i \frac{3}{2}, csc (x) = - \frac{1}{2} - i \frac{3}{2}

csc (x) = 1 : x = \frac{π}{2} + 2 πn

csc (x) = - \frac{1}{2} + i \frac{3}{2} :

No Solution

csc (x) = - \frac{1}{2} - i \frac{3}{2} :

No Solution

Combine all the solutions

x = \frac{π}{2} + 2 πn

cos (θ) = \frac{4}{7}, tan (θ) < 0

tan (θ) = \frac{4}{2}

e^{s i n (x)} - e^{- s i n (x)} = 2

cos (x) \cdot sec (x) \cdot cot^{2} (x) = csc^{2} (x)

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

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