Find the exact value of

Question

Sin ( sin-1. 9/41 - cos-1 (-5/13)

Answer 1

let sin-1. 9/41 = ß and cos-1 (-5/13 = Ø
so sin ß = 9/41 and cos ß = 40/41
and cosØ = -5/13 and sinØ = 12/13

then Sin ( sin-1. 9/41 - cos-1 (-5/13)
= sin(ß - Ø)
= sinßcosØ - cosßsinØ
= (9/41)(-5/13) - (40/41)(12/13) = -525/533