If cos (x - y) \(=\frac{\sqrt 3}{2}\) and sin (x + y) \(=\frac{1}{2

1.	If cos (x - y) \(=\frac{\sqrt 3}{2}\) and sin (x + y) \(=\frac{1}{2}\), then the value of x (0 ≤ x ≤ 90) is:1. 45° 2. 30°3. 15°4. 60°
Answer» Correct Answer - Option 2 : 30° Given: cos (x - y) = √3/2 sin (x + y) = 1/2 Formula: cos30° = √3/2 sin30° = 1/2 Calculation: cos(x - y) = √3/2 ⇒ cos(x - y) = cos30° (x - y) = 30° ---- (1) sin(x + y) = 1/2 ⇒ sin(x + y) = sin30° (x + y) = 30 ---- (2) Add equation (1) and equation (2), we get 2x = 60° ∴ x = 30°

If cos (x - y) \(=\frac{\sqrt 3}{2}\) and sin (x + y) \(=\frac{1}{2}\), then the value of x (0 ≤ x ≤ 90) is:1. 45° 2. 30°3. 15°4. 60°

Answer» Correct Answer - Option 2 : 30°

Given:

cos (x - y) = √3/2

sin (x + y) = 1/2

Formula:

cos30° = √3/2

sin30° = 1/2

Calculation:

cos(x - y) = √3/2

⇒ cos(x - y) = cos30°

(x - y) = 30° ---- (1)

sin(x + y) = 1/2

⇒ sin(x + y) = sin30°

(x + y) = 30 ---- (2)

Add equation (1) and equation (2), we get

2x = 60°

∴ x = 30°