Question

In a triangle ABC, with usual notations ∠A = 60°, then (1 + $\frac {a}{c}$ + $\frac {b}{c}$)(1 + $\frac {c}{b}$ - $\frac {a}{b}$) = ?

• A. 3
• B. $\frac {1}{2}$
• C. $\frac {3}{2}$
• D. 1

Answer 1

Answer: (A)

3

Answer 2

(1 + $\frac {a}{c}$+ $\frac {b}{c}$ )(1 + $\frac {c}{b}$ - $\frac {a}{b}$)
= (\frac {c + a + b}{c})$$(\frac {(b+c-a}{b})
= $\frac {(b+c)^2 - a^2}{bc}$
= $\frac {(b^2 + c^2 - a^2) + 2bc}{bc}$
= $\frac {b^2 +c^2 -a^2}{bc}$ + 2
= $\frac {2(b^2 +c^2 -a^2)}{bc}$ + 2
= 2 cos A +2
Here, cos 60o = $\frac {1}{2}$
Then,
= 2 x $\frac {1}{2}$ +2
= 1+2
= 3

Therefore, the correct option is (A) 3.