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Question
Prove that : `2sin^-1 (3/5) -tan^-1 (17/31) = pi/4.`
Solution
LHS: `2sin^-1 ((3)/(5))-tan^-1 ((17)/(31))`
`= 2tan^-1(3/4) - tan^-1(17/31)`
= `tan^-1 ((6/(4))/(1-9/16)) - tan^-1 (17)/(31)`
⇒ = `tan^-1 (24)/(7) - tan^-1 (17)/(31)`
= `tan^-1 ((24/7 - 17/34)/(1+ 24/7 xx 17/31))`
= `tan^-1 ((625)/625)`
= `tan^-1 (1)`
= `pi/(4) = "RHS"`.
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