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

The general solution for 2sin(x)=csc(x) is x= pi/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin,x=(7pi)/4+2pin

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2sin(x)=csc(x)

2 sin (x) = csc (x)

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Solution steps

2 sin (x) = csc (x)

Subtract

csc (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

csc (x) = 2, csc (x) = - 2

csc (x) = 2 : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

csc (x) = - 2 : x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combine all the solutions

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

1 + tan (x) = sec (x)

sin (2 x) = cos (6 0^{\circ})

tan (x) = \frac{1}{- 3}

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

sin (\frac{x}{2}) = \frac{1}{2}

What is the general solution for 2sin(x)=csc(x) ?
The general solution for 2sin(x)=csc(x) is x= pi/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin,x=(7pi)/4+2pin