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Question
If tan A = `5/6, tan "B" = 1/11`, prove that A + B = `pi/4`
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Solution
We have, tan A = `5/6` and tan B = `1/11`
∴ tan(A + B) = `(tan"A" + tan"B")/(1 - tan"A".tan"B")`
∴ tan(A + B) = `(5/6 + 1/11)/(1 - (5/6)(1/11))`
∴ tan(A + B) = `(55 + 6)/(66 - 5)`
∴ tan(A + B) = `61/61`
∴ tan(A + B) = 1
∴ tan(A + B) = 1 = `tan π/4`
∴ A + B = `π/4`
Hence proved.
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