What is the general solution for sin(x)-csc(x)+1=0 ?

The general solution for sin(x)-csc(x)+1=0 is x=0.66623…+2pin,x=pi-0.66623…+2pin

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

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

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

csc (x) = - \frac{- 1 + 5}{2}, csc (x) = \frac{1 + 5}{2}

csc (x) = - \frac{- 1 + 5}{2} :

No Solution

csc (x) = \frac{1 + 5}{2} : x = arccsc (\frac{1 + 5}{2}) + 2 πn, x = π - arccsc (\frac{1 + 5}{2}) + 2 πn

Combine all the solutions

x = arccsc (\frac{1 + 5}{2}) + 2 πn, x = π - arccsc (\frac{1 + 5}{2}) + 2 πn

Show solutions in decimal form

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

tan^{2} (θ) - sec^{2} (θ) = cos (- θ)

- 2 sin (t) - 4 cos (2 t) = 0

8 sin (2 x) - 43 = 0

cos (3 x) cos (9 x) + sin (3 x) sin (9 x) = 0

cos (2 x) + 5 sin (x) + 2 = 0, 0 \leq x < 2 π

What is the general solution for sin(x)-csc(x)+1=0 ?
The general solution for sin(x)-csc(x)+1=0 is x=0.66623…+2pin,x=pi-0.66623…+2pin