If \(\sin \left( {A - B} \right) = \frac{1}{2}\) and \(\cos \left(

1.	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°
Answer» 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°

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°

Answer» 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°