What is the general solution for csc(x)-3=-2sin(x) ?

The general solution for csc(x)-3=-2sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin,x= pi/2+2pin

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csc(x)-3=-2sin(x)

csc (x) - 3 = - 2 sin (x)

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

csc (x) - 3 = - 2 sin (x)

Subtract

- 2 sin (x)

from both sides

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

Rewrite using trig identities

- 3 + csc (x) + \frac{2}{csc ( x )} = 0

Solve by substitution

csc (x) = 2, csc (x) = 1

csc (x) = 2 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

csc (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

\frac{sin ( y )}{80} = \frac{sin ( 4 0 ^{\circ} )}{60}

cos (w) = 0.75 sin (9 0^{\circ} - w)

csc (4 x) = 2

3 tan^{2} (x) = 2 sec^{2} (x) + 1, 0^{\circ} \leq x \leq 18 0^{\circ}

2 arctan (x e^{\frac{0}{2}}) = \frac{π}{2}

What is the general solution for csc(x)-3=-2sin(x) ?
The general solution for csc(x)-3=-2sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin,x= pi/2+2pin