Last help with trig

sin (u/2)  =  sqrt [    (1 - cos (u) )  / 2 ] =   sqrt [ ( 1 - sqrt (15)/5) / 2 ] =

sqrt [ [ 5 - sqrt (15)] / 10 ]

cos (u/2)    =  sqrt [    (1 + cos (u) )  / 2 ] =   sqrt [ ( 1 + sqrt (15) / 5) / 2 ] =

sqrt [ [ 5 + sqrt (15)] / 10 ]

tan (u/2)   =  sin (u/2) /  cos (u/2)    =

sqrt [ [ 5 - sqrt (15)] / 10 ]  /  sqrt [ [ 5 + sqrt (15)] / 10 ]  =

sqrt  [ 5 - sqrt (15)]    /  sqrt  [ 5 + sqrt (15)]