question_answer

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

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

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

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

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

E) None of these