Question : If $\cos (A-B)=\frac{\sqrt{3}}{2}$, and $\cos (A+B)=0$, where $A$ and $B$ are positive acute angles and $A \geq B$, then the measures of $A$ and $B$ are:
Option 1: 80° and 10°
Option 2: 60° and 30°
Option 3: 70° and 20°
Option 4: 50° and 40°

Question

Question : If $\cos (A-B)=\frac{\sqrt{3}}{2}$, and $\cos (A+B)=0$, where $A$ and $B$ are positive acute angles and $A \geq B$, then the measures of $A$ and $B$ are:

Option 1: 80° and 10°

Option 2: 60° and 30°

Option 3: 70° and 20°

Option 4: 50° and 40°

Team Careers360 · Accepted Answer

Correct Answer: 60° and 30°

Solution : Given, $\cos (A-B)=\frac{\sqrt{3}}{2}$ and $\cos (A+B)=0$
Since $A$ and $B$ are acute positive angles,
$\cos (A-B)=\frac{\sqrt{3}}{2}$
⇒ $(A-B) = \cos^{-1} \frac{\sqrt{3}}{2}$
⇒ $(A-B) = 30°$ ------------------ (1)
$\cos (A+B)=0$
⇒ $(A+B) = \cos^{-1} 0$
⇒ $(A+B) = 90°$ --------------------- (2)
Solving (1) and (2), we get,
$A = 60°$ and $B = 30°$
Hence, the correct answer is 60° and 30°.

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Question : If cos⁡(A−B)=32, and cos⁡(A+B)=0, where A and B are positive acute angles and A≥B, then the measures of A and B are:Option 1: 80° and 10°Option 2: 60° and 30°Option 3: 70° and 20°Option 4: 50° and 40°

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Question : If $\cos (A - B) = \frac{\sqrt{3}}{2}$ , and $\cos (A + B) = 0$ , where $A$ and $B$ are positive acute angles and $A \geq B$ , then the measures of $A$ and $B$ are:
Option 1: 80° and 10°
Option 2: 60° and 30°
Option 3: 70° and 20°
Option 4: 50° and 40°