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Question
Prove `tan^(-1) 2/11 + tan^(-1) 7/24 = tan^(-1) 1/2`
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Solution
To prove: `tan^(-1) 2/11 + tan^(-1) 7/24 = tan^(-1) 1/2`
L.H.S =` tan^(-1) 2/11 + tan^(-1) 7/24`
`= tan^(-1) (2/11 + 7/24)/(1-2/11. 7/24)` `[tan^(-1) x + tan^(-1) y = tan^(-1) (x + y)/(1 - xy)]`
= tan^(-1) `((48+77)/(11xx24))/((11xx24 - 14)/(11xx24))`
`= tan^(-1) (48 + 77)/(264 - 14) = tan^(-1) 125/250 = tan^(-1) 1/2 =` R.H.S
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