Question : If $\tan (A + B) = \sqrt{3}$ , and $\tan (A - B) = \frac{1}{\sqrt{3}}$ , $∠ A + ∠ B < 90 °$ ; $A \geq B$ then $∠ A$ is:
Option 1: 90°
Option 2: 30°
Option 3: 45°
Option 4: 60°

Question

Question : If $A = \cot 30^{\circ} \tan 60^{\circ} + \cot 60^{\circ} \tan 30^{\circ}$ , then what is the value of A?

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Answer 1

Correct Answer: 45°

Solution : Given: $\tan (A + B) = \sqrt{3}$
⇒ $A + B = 60 °$ ------(1)
$\tan (A - B) = \frac{1}{\sqrt{3}}$
⇒ $A - B = 30 °$ ------(2)
Adding equations (1) and (2), we have,
$2 A = 90 °$
$∴ A = 45 °$
Hence, the correct answer is 45°.

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Question : If tan⁡(A+B)=3, and tan⁡(A−B)=13, ∠A+∠B<90°; A≥B then ∠A is:Option 1: 90°Option 2: 30°Option 3: 45°Option 4: 60°

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Question : If $\tan (A + B) = \sqrt{3}$ , and $\tan (A - B) = \frac{1}{\sqrt{3}}$ , $∠ A + ∠ B < 90 °$ ; $A \geq B$ then $∠ A$ is:
Option 1: 90°
Option 2: 30°
Option 3: 45°
Option 4: 60°