Find real part of z=tan(a+ib)

Dear ashish

z=tan(a+ib)

  let z = x+iy

so 

 x+iy = tan(a+ib)

x-iy = tan (a-ib)

add

 2x = tan(a+ib)  + tan (a-ib)

       =sin ( a+ib+a -ib)/2cos(a+ib)cos(a-ib)

       = sin2a / (cos2a + cos2ib)

      = sin2a/(cos2a + cosh2b)

x = sin2a/2(cos2a + cosh2b) 

 in above derivation we use cosi2b = cosh2b

  this a formula  and cosh2b is a real value,not imaginarry

  coshx =(e^x + e^-x )/2

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