question_answer

In a\[\Delta PQR,\angle R=\frac{\pi }{2}\]If\[\tan \left( \frac{P}{2} \right)\]and\[\tan \left( \frac{Q}{2} \right)\]are the roots of\[a{{x}^{2}}+bx+c=0,a\ne 0,\]then     AIEEE  Solved  Paper-2005

A) \[d=a+c\]          

B) \[b=c\]

C) \[c=a+b\]           

D) \[a=o+c,\]

Correct Answer: C

Solution :

Since,andare roots of equation                             ...(i) and                                    ...(ii) Also,      (as P, Q, R are angles of a triangle) Now,       [from Eqs. (i) and (ii)] Alternate Solution            [from Eqs. (i) and (ii)]