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Question
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
Solution
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
L.H.S
`=cos^-1 (1-2 xx9/25)-tan^-1(17/31)`
`=cos^-1 (7/25) - tan^-1 (17/31)`
`=tan^-1 (24/7)-tan^-1(17/31)`
`=tan^-1 ((24/7-17/31)/(1+42/7xx17/31))`
`=tan^-1((24xx31-17xx7)/(31xx7+24xx17))`
`=tan^-1 (625/625)`
`=tan^(-1) 1`
`=pi/4`
Hence Proved
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