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Question
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
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Solution
Given A + B = 45°
tan(A + B) = tan 45°
`(tan "A" + tan "B")/(1 - tan "A" tan "B")` = 1
tan A + tan B = 1 – tan A . tan B ......(1)
(1 + tan A)(1 + tan B) = 1 + tan B + tan A + tan A tan B
= 1 + (tan A + tan B) + tan A tan B
= 1 + 1 – tan A tan B + tan A tan B ......(By equation (1))
= 2
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