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Question
Show that `tan^-1 (1/2) + tan^-1 (2/11) = tan^-1 (3/4)`
Solution
We know that tan-1 x + tan-1 y = `tan^-1 ((x + y)/(1 - xy))`
Now LHS = `tan^-1 (1/2) + tan^-1 (2/11)`
`= tan^-1 ((1/2 + 2/11)/(1 - 1/2 xx 2/11))`
`= tan^-1 (((11 + 4)/22)/(1 - 1/11))`
`= tan^-1 ((15/22)/(10/11))`
`= tan^-1 (15/22 xx 11/10)`
`= tan^-1 ((3 xx 1)/(2 xx 2))`
`= tan^-1 (3/4)` = RHS
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