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NIST
4 Elementary FunctionsTrigonometric Functions

§4.22 Infinite Products and Partial Fractions

4.22.1 sinz =zn=1(1-z2n2π2),
4.22.2 cosz =n=1(1-4z2(2n-1)2π2).

When znπ, n,

4.22.3 cotz =1z+2zn=11z2-n2π2,
4.22.4 csc2z =n=-1(z-nπ)2,
4.22.5 cscz =1z+2zn=1(-1)nz2-n2π2.