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प्रश्न
Prove that `tan^-1 2/11 + tan^-1 7/24 = tan^-1 1/2`
उत्तर
`tan^-1"A" + tan^-1"B" = tan^-1 (("A" + "B")/(1 - "AB"))`
`tan^-1 (2/11) + tan^-1 (7/24) = tan^-1 ((2/11 + 7/24)/(1- 2/11 * 7/24))`
= `tan^-1 (((48 + 77)/(11 xxx 24))/((264 - 14)/(11 xx 24)))`
= `tan^-1 (125/250)`
= `tan^-1(1/2)`
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