Question : If $\sin (p+q)=1$ and $\cos (p-q)=\frac{\sqrt{3}}{2}$, then find $p$.
Option 1: 90°
Option 2: 80°
Option 3: 60°
Option 4: 120°
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Correct Answer: 60°
Solution : Given: $\sin (p+q)=1$ and $\cos (p-q)=\frac{\sqrt{3}}{2}$ $\sin (p+q)=\sin 90°$ and $\cos (p-q)=\cos 30°$ ⇒ $(p+q)=90°$ ------------(1) And $(p-q)=30°$ --------- (2) Adding equations (1) and (2), we have, ⇒ $2p=120°$ ⇒ $p=60°$ Hence, the correct answer is 60°.
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