If \(\cos (x-y)=\displaystyle\frac{\sqrt{3}}{2}\) and \(\sin (x+y)=1\) where \(x > y\), then the value of \(y\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 30°
Turn each given value into an angle using the standard values \(\cos30^\circ=\displaystyle\frac{\sqrt{3}}{2}\) and \(\sin90^\circ=1\), then solve the two equations together.
\(x-y=30^\circ\) (1)
\(x+y=90^\circ\) (2)
Subtracting (1) from (2), \(x\) cancels: \(2y=60^\circ\), so \(y=\) 30°