If ABCD is a cyclic quadrilateral such that 3 tan A +4=0 and 13 cos B +5=0, then a quadratic equation whose roots are tan C and tan D, is

Question

If ABCD is a cyclic quadrilateral such that 3 tan A +4=0 and 13 cos B +5=0, then a quadratic equation whose roots are tan C and tan D, is (A) 15 x2-56 x+48=0 (B) x2-18 x+1=0 (C) 12 x2-17 x+29 (D) None of these

Tardigrade Admin · Accepted Answer

tan A =-(4/3) ; ∵ A + C =π ⇒ tan C =(4/3) cos B =(-5/12) ; and B + D =π ⇒ cos D =(5/13) ⇒ tan D =(12/5) ∴ Equation are (x-(4/3))(x-(12/5))=0

Q. If $A BC D$ is a cyclic quadrilateral such that $3 tan A + 4 = 0$ and $13 cos B + 5 = 0$ , then a quadratic equation whose roots are $tan C$ and $tan D$ , is

$15 x^{2} - 56 x + 48 = 0$

$x^{2} - 18 x + 1 = 0$

$12 x^{2} - 17 x + 29$

None of these

$tan A = - \frac{4}{3}; ∵ A + C = π \Rightarrow tan C = \frac{4}{3}$ $cos B = \frac{- 5}{12};$ and $B + D = π \Rightarrow cos D = \frac{5}{13} \Rightarrow tan D = \frac{12}{5}$
$∴$ Equation are $(x - \frac{4}{3}) (x - \frac{12}{5}) = 0$

Q. If ABCD is a cyclic quadrilateral such that 3tanA+4=0 and 13cosB+5=0, then a quadratic equation whose roots are tanC and tanD, is

15x2−56x+48=0

x2−18x+1=0

12x2−17x+29