Asked by Anonymous
find the exact value of tan(2sin-1 3/5)
Answers
Answered by
Reiny
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
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
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