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

The general solution for 2sin(x)-csc(x)=2 is x=-0.37473…+2pin,x=pi+0.37473…+2pin

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

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

x = - 0.37473 \dots + 2 πn, x = π + 0.37473 \dots + 2 πn

Solution steps

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

Subtract

2

from both sides

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

Rewrite using trig identities

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

Solve by substitution

csc (x) = - 1 - 3, csc (x) = 3 - 1

csc (x) = - 1 - 3 : x = arccsc (- 1 - 3) + 2 πn, x = π + arccsc (1 + 3) + 2 πn

csc (x) = 3 - 1 :

No Solution

Combine all the solutions

x = arccsc (- 1 - 3) + 2 πn, x = π + arccsc (1 + 3) + 2 πn

Show solutions in decimal form

x = - 0.37473 \dots + 2 πn, x = π + 0.37473 \dots + 2 πn

5 cos (θ) - 3 = 0

(cos (x)) (sin (x)) = - 1

- 2 tan (x) sec^{2} (x) = 0

2 - sin (x) = sin (x)

cos^{2} (t) = \frac{1}{2}

What is the general solution for 2sin(x)-csc(x)=2 ?
The general solution for 2sin(x)-csc(x)=2 is x=-0.37473…+2pin,x=pi+0.37473…+2pin