What is the general solution for 2sin(x)-csc(x)=1 ?

The general solution for 2sin(x)-csc(x)=1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/2+2pin

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2sin(x)-csc(x)=1

2 sin (x) - csc (x) = 1

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

2 sin (x) - csc (x) = 1

Subtract

1

from both sides

2 sin (x) - csc (x) - 1 = 0

Rewrite using trig identities

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

Solve by substitution

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

csc (x) = - 2 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

csc (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

2 cos^{2} (x) + 3 cos (x) = 0

2 sin^{3} (x) - sin (x) = 0

(cos (3 θ)) (cos (θ)) - 1 = (sin (3 θ)) (sin (θ))

tan (θ) = - 5

tan^{4} (x) - 13 tan^{2} (x) + 36 = 0

What is the general solution for 2sin(x)-csc(x)=1 ?
The general solution for 2sin(x)-csc(x)=1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/2+2pin