If cos(x +y)=1/2 and sin(x—y) = 0, where x and y are positive acute angles and x ≥ y, then x and y are:

Correct option is D

Given:
cos (x + y) = 1/2
sin (x - y) = 0
Concept Used:
sin x = sin y then x = y
cos x = cos y then x= y
Where 0 ≤ x, y ≤ 90°
Formula Used:
cos 60° = 1/2, sin 0° = 0

Solution:
We have
cos (x + y) = 1/2
=> cos (x + y) = cos 60°
=> x + y = 60° -----(i)
And sin (x - y) = 0
=> sin (x - y) = sin 0°
=> x - y = 0° -----(ii)
On adding equation (i) and (ii), we get
2x = 60°
=> x = 30°
Now, From (i)
30° + y = 60°
=> y = 30°
So, the value of x and y are 30° and 30° respectively.