In ΔABC with the usual notations, if tanA/2tanB/2=3/4 then a+b= …

Correct answer: (C) 7c. We have, In ΔABC tanA/2tanB/2=3/4 ⇒√(s-bs-css-a)√(s-as-css-b)=3/4 ⇒√(s-bs-cs-as-css-a.ss-b)=3/4 ⇒(s-c)/s=3/4⇒(a+b+c)/2-c(a+b+c)/2=3/4 ⇒(a+b-c)/(a+b+c)=3/4 ⇒4a+4b-4c=3a+3b+3c ⇒a+b=7c

Q72 / 150 · MHT CET 2019 (Shift 1) · Mathematics

In $Δ A B C$ with the usual notations, if $(t a n \frac{A}{2}) (t a n \frac{B}{2}) = \frac{3}{4}$ then $a + b =$ …

A
4c
B
2c
Correct answer
C
7c
D
3c

Solution

We have, In

Δ A B C

(t a n \frac{A}{2}) (t a n \frac{B}{2}) = \frac{3}{4}

\Rightarrow \sqrt{\frac{(s - b) (s - c)}{s (s - a)}} \sqrt{\frac{(s - a) (s - c)}{s (s - b)}} = \frac{3}{4}

\Rightarrow \sqrt{\frac{(s - b) (s - c) (s - a) (s - c)}{s (s - a) . s (s - b)}} = \frac{3}{4}

\Rightarrow \frac{(s - c)}{s} = \frac{3}{4} \Rightarrow \frac{\frac{a + b + c}{2} - c}{\frac{a + b + c}{2}} = \frac{3}{4}

\Rightarrow \frac{a + b - c}{a + b + c} = \frac{3}{4}

\Rightarrow 4 a + 4 b - 4 c = 3 a + 3 b + 3 c

\Rightarrow a + b = 7 c

Hence, the correct answer is option: 'C'.

In ΔABC with the usual notations, if tanA2tanB2=34 then a+b= …

Solution

Relevant Questions

In $Δ A B C$ with the usual notations, if $(t a n \frac{A}{2}) (t a n \frac{B}{2}) = \frac{3}{4}$ then $a + b =$ …