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Question
Show that `2sin^-1(3/5) = tan^-1(24/7)`
Sum
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Solution
Let x = `sin^(-1)(3/5)`
sin x = `3/5`
tan x = `(3/4)`
x = `tan^(-1)(3/4)`
`sin^(-1)(3/5) = tan^(-1)(3/4)`
`2sin^(-1)(3/5) = 2tan^(-1)(3/4)`
= `tan^(-1)(3/4) + tan^(-1)(3/4)`
= `tan^(-1)(((3/4) + (3/4))/(1 - 3/4(3/4)))`
= `tan^(-1)((6/4)/(7/16))`
= `tan^(-1)(6/4 xx 16/7)`
= `tan^(-1)(24/7)`
`sin^(-1)(3/5) = tan^(-1)(24/7)`
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