What is the general solution for e^{sin(x)}-e^{-sin(x)}=2 ?

The general solution for e^{sin(x)}-e^{-sin(x)}=2 is x=1.07876…+2pin,x=pi-1.07876…+2pin

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e^{sin(x)}-e^{-sin(x)}=2

e^{s i n (x)} - e^{- s i n (x)} = 2

x = 1.07876 \dots + 2 πn, x = π - 1.07876 \dots + 2 πn

Solution steps

e^{s i n (x)} - e^{- s i n (x)} = 2

Solve by substitution

sin (x) = ln (1 + 2)

sin (x) = ln (1 + 2) : x = arcsin (ln (1 + 2)) + 2 πn, x = π - arcsin (ln (1 + 2)) + 2 πn

Combine all the solutions

x = arcsin (ln (1 + 2)) + 2 πn, x = π - arcsin (ln (1 + 2)) + 2 πn

Show solutions in decimal form

x = 1.07876 \dots + 2 πn, x = π - 1.07876 \dots + 2 πn

cos (x) \cdot sec (x) \cdot cot^{2} (x) = csc^{2} (x)

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

(cos (x) - 1) (3 cot (x) + 1) = 0

4 cot (x) = 3 csc (x)

x, sin (2 x) - cos (x) = 0

What is the general solution for e^{sin(x)}-e^{-sin(x)}=2 ?
The general solution for e^{sin(x)}-e^{-sin(x)}=2 is x=1.07876…+2pin,x=pi-1.07876…+2pin