Find the exact value of the expression sin 2 cos 1 513 sin 2

Find the exact value of the expression. sin (2 cos -1 5/13) sin (2 cos -1(5/13) =

Solution

sin(2cos^-1(5/13))

let cos^-1(5/13)=p =>cosp=5/13=>sinp=(13²-5²)/13=12/13

sin(2p)=2sinp cosp

sin2p=2(12/13)(5/13)

sin2p =120/169

ttherefore sin(2cos^-1(5/13))=120/169