Trigonometric EquationHard
Question
In a triangle PQR ∠R =
, if tan
and tan
are the roots of the equation ax2 + bx + c = 0(a ≠ 0), then
, if tan and tan are the roots of the equation ax2 + bx + c = 0(a ≠ 0), then Options
A.a + b = c
B.a + b = c
C.a + c = b
D.b = c
Solution
It is given that tan (P / 2) and tan (Q / 2) are the roots of the quadratic equation
ax2 + bx + c = 0 and ∠R = π / 2
∴ tan (P / 2) + tan (Q / 2) = - b / a
and tan (P / 2) tan (Q / 2) = c / a
Since, P + Q + R = 180o
⇒ P + Q = 90o
⇒
= 45o
⇒ tan
= tan 45o
⇒
⇒
= 1
⇒
= 1 ⇒ 
= 1
⇒ - b = a - c
⇒ a + b = c
ax2 + bx + c = 0 and ∠R = π / 2
∴ tan (P / 2) + tan (Q / 2) = - b / a
and tan (P / 2) tan (Q / 2) = c / a
Since, P + Q + R = 180o
⇒ P + Q = 90o
⇒
= 45o⇒ tan
= tan 45o⇒
⇒
= 1⇒
= 1 ⇒ = 1⇒ - b = a - c
⇒ a + b = c
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