Question : If $\tan (A + B) = \sqrt{3}$ and $\tan (A - B) = \frac{1}{\sqrt{3}}; 0 ° < (A + B) < 90 °; A > B$ , then the values of $A$ and $B$ are respectively:
Option 1: 45° and 15°
Option 2: 15° and 45°
Option 3: 30° and 30°
Option 4: 60° and 30°

Question

Question : What is the value of $\frac{\tan 45^{\circ} - \tan 15^{\circ}}{1 + \tan 45^{\circ} \tan 15^{\circ}}$ ?

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Answer 1

Correct Answer: 45° and 15°

Solution : Given: $\tan (A + B) = \sqrt{3}$ and $\tan (A - B) = \frac{1}{\sqrt{3}}$
$\tan (A + B) = \sqrt{3} = \tan 60 °$
⇒ $A + B = 60 °$ .........................(1)
Also, $\tan (A - B) = \frac{1}{\sqrt{3}} = \tan 30 °$
⇒ $A - B = 30 °$ ............................(2)
Solving equations (1) and (2) we get,
$A = 45 °$ and $B = 15 °$
Hence, the correct answer is 45° and 15°.

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Question : If tan⁡(A+B)=3 and tan⁡(A−B)=13;0°<(A+B)<90°;A>B, then the values of A and B are respectively:Option 1: 45° and 15°Option 2: 15° and 45°Option 3: 30° and 30°Option 4: 60° and 30°

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Question : If $\tan (A + B) = \sqrt{3}$ and $\tan (A - B) = \frac{1}{\sqrt{3}}; 0 ° < (A + B) < 90 °; A > B$ , then the values of $A$ and $B$ are respectively:
Option 1: 45° and 15°
Option 2: 15° and 45°
Option 3: 30° and 30°
Option 4: 60° and 30°