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Question
If tan(A - B) = `(1)/sqrt(3)` and tan(A + B) = `sqrt(3)`, find A and B.
Solution
tan(A - B) = `(1)/sqrt(3)`
⇒ tan(A - B) = tan30°
⇒ A - B = 30° ......(i)
tan(A + B) = `sqrt(3)`
⇒ tan(A + B) = tan60°
⇒ A + B = 60° ........(ii)
Adding (i) and (ii)
A - B + A + B = 30° + 60°
⇒ 2A = 90°
⇒ A = 45°
Substituting value of A in (i)
A - B = 30°
45° - B = 30°
B = 15°
Therefore,
A = 45° and B = 15°.
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