find the exact value of tan(2sin-1 3/5)

Answer 1

let sin^-1 (3/5) = Ø

then sinØ = 3/5 and cosØ = 4/5

so you want tan 2Ø
= sin2Ø/cos2Ø
= 2sinØcosØ/(2cos^2Ø - 1)
= 2(3/5)(4/5)/(32/25 - 1)
=(24/25) / (7/25)
= (24/25)(25/7)
= 24/7