Question

In a triangle ABC, ŠC = $\frac{\pi}{2}$. If tan $\left( \frac{A}{2} \right)$and tan$\left( \frac{B}{2} \right)$are the roots of the equation ax² + bx + c = 0 (a ¹ 0) then

• A. a + b = c
• B. b + c = a
• C. a + c = b
• D. b = c

Answer 1

Answer: (A)

a + b = c

Answer 2

tan $\frac{A}{2}$ + tan $\frac{B}{2}$ = – b/a ...(i)

tan $\frac{A}{2}$.tan $\frac{B}{2}$ = c/a ...(ii)

A + B = p/2 Ž $\frac{A}{2}$ + $\frac{B}{2}$ = p/4

Ž tan ($\frac{A}{2}$ + $\frac{B}{2}$) = 1

–b/a/1 – c/a = 1 Ž b = c – a

Ž a + b = c