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

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

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csc(x)=sin(x)

csc (x) = sin (x)

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

Solution steps

csc (x) = sin (x)

Subtract

sin (x)

from both sides

csc (x) - sin (x) = 0

Rewrite using trig identities

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

Solve by substitution

csc (x) = 1, csc (x) = - 1

csc (x) = 1 : x = \frac{π}{2} + 2 πn

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

Combine all the solutions

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

tan (2 x + \frac{π}{3}) = 0

18 cos^{2} (x) = 9

\frac{1}{cot ( x )} - \frac{sec ( x )}{csc ( x )} = cos (x)

10 sin (x) + 10 cos^{2} (x) = 10, 0 \leq x < 2 π

sin (x) = 1, 2 π \leq x \leq 4 π

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