find the exact value of sinarctan 14Solutionsinarctan 14 let

find the exact value of sin(arctan (1/4))

Solution

sin(arctan (1/4))

let arctan (1/4) =u

=>tanu =1/4

=>sinu =1/[1²+4²]

=>sinu =1/17

=>u=arcsin(1/17)

sin(arctan (1/4))

=sin(u)

=sin(arcsin(1/17))

=1/17