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Popular >

solvefor x,e^{cos(y)}-e^{sin(x)}=sin(y)

Solution

solve for

x, e^{c o s (y)} - e^{s i n (x)} = sin (y)

Solution

x = arcsin (ln (- sin (y) + e^{c o s (y)})) + 2 πn, x = π + arcsin (- ln (- sin (y) + e^{c o s (y)})) + 2 πn

Solution steps

e^{c o s (y)} - e^{s i n (x)} = sin (y)

Move

e^{c o s (y)}

to the right side

- e^{s i n (x)} = sin (y) - e^{c o s (y)}

Divide both sides by

- 1

e^{s i n (x)} = - sin (y) + e^{c o s (y)}

Apply exponent rules

sin (x) = ln (- sin (y) + e^{c o s (y)})

Apply trig inverse properties

x = arcsin (ln (- sin (y) + e^{c o s (y)})) + 2 πn, x = π + arcsin (- ln (- sin (y) + e^{c o s (y)})) + 2 πn

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