Find the exact value of the expression tan sin1 3 4 cos1 1

Find the exact value of the expression. tan ( sin^1 3/ 4 cos^1 1/ 5 show all work

tan ( sin^1 3/ 4 cos^1 1/ 5)

let x= sin^-1(3/4)

sinx = 3/4 ----> tanx = 3/sqrt(7)

let y = cos^-1(1/5)

cosy = 1/5

tany = sqrt(24)

tan ( sin^1 3/ 4 cos^1 1/ 5) = tan(x+y)

= (tanx +tany)/( 1-tanx*tany)

=( 3/sqrt17 +sqrt24)/( 1-3sqrt(24/17) )

= (3+ sqrt(408)/[sqrt(17) -3sqrt(24)]

= (3 +sqrt(408)/[ sqrt(17) - 3sqrt(24) ]