If \(\sin \left( {A – B} \right) = \frac{1}{2}\) and \(\cos \left( {A + B} \right) = \frac{1}{2}\), where A > B > 0° and A + B is an acute angle, then the value of A is:
1. 30°
2. 60°
3. 45°
4. 15°
1. 30°
2. 60°
3. 45°
4. 15°
Correct Answer – Option 3 : 45°
Given:
sin(A – B) = 1/2
Calculation:
We know that
sin 30° = 1/2
sin(A – B) = sin 30°
⇒ A – B = 30° —-(i)
Also, cos(A + B) = 1/2
cos 60° = 1/2
cos(A + B) = cos 60°
⇒ A + B = 60° —-(ii)
Adding (i) and (ii)
2A = 90°
⇒ A = 45°
∴ The value of A is 45°