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Question
If tan `"A" = (1)/(2), tan "B" = (1)/(3) and tan("A" + "B") = (tan"A" + tan"B")/(1 - tan"A" tan"B")`, find A + B.
Solution
Since tan `"A" = (1)/(2), tan "B" = (1)/(3)`
tan(A + B) = `(tan"A" + tan"B")/(1 - tan"A" tan"B")`
⇒ tan(A + B) = `(1/2 + 1/3)/(1 - (1/2 xx 1/3))`
⇒ tan(A + B) = `(5/6)/(1 - 1/6)`
⇒ tan(A + B) = `(5/6)/(5/6)`
⇒ tan(A + B) = 1
⇒ tan(A + B) = tan45°
⇒ A + B = 45°.
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