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)]