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Question
Prove that `tan^-1 1/4 + tan^-1 2/9 = sin^-1 1/sqrt(5)`
Solution
L.H.S. = `tan^-1 1/4 + tan^-1 2/9`
= `tan^-1 (1/4 + 2/9)/(1 - 1/4 * 2/9)`
= `tan^-1 (9 + 8)/(36 - 2)`
= `tan^-1 1/2`
= `sin^-1 1/sqrt(5)`.
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