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## Homework Statement

Find and classify the singular point for

f(z) = 1/ ( sin z - sin a)

Where a is an arbitrary real constant.

## Homework Equations

f(z) = 1/ ( sin z - sin a)

Where a is an arbitrary real constant.

## The Attempt at a Solution

There will be infinite number of singularities of sin z = sin a

Put z' = z-a

Denominator can be written as sin z - sin a = sin ( z'+ a) - sin a

= sin a cos z' + cos a sin z' - sin a = sin a ( cos z' - 1) + cos a sin z'

= sin a ( -1/2! Z'^ 2 + 1/4! Z'^ 4 + ......) + cos a ( z' - z'^ 3/3! +......)

= cos a z' - 1/2! Sin a z'^2 -.........

Now how to define a and singularities ??