question_answer

In an acute angled triangle PQR, if\[\sqrt{2}\,\sin \,(P+Q-R)=1\] and \[\tan \,(Q+R-P)=\sqrt{3},\]find the values of P, Q and R.

A)  \[P=50{}^\circ ,Q=42\,\,\frac{1{}^\circ }{2},R=87\,\,\frac{1{}^\circ }{2}\]

B)  \[P=52\,\,\frac{1{}^\circ }{2},Q=67\,\,\frac{1{}^\circ }{2},R=60{}^\circ \]

C)  \[P=37\,\,\frac{1{}^\circ }{2},Q=90{}^\circ ,R=52\,\,\frac{1{}^\circ }{2}\]

D)  \[P=90{}^\circ ,Q=37\,\,\frac{1{}^\circ }{2},R=52\,\,\frac{1{}^\circ }{2}\]

E)  None of these