If,in a triangle ABC,tan frac{A}{2} = frac{5} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) We know that $	an \frac{A}{2} = \sqrt{\frac{(s-b)(s-c)}{s(s-a)}}$ and $	an \frac{C}{2} = \sqrt{\frac{(s-a)(s-b)}{s(s-c)}}$.Multiplying these,we

Vedclass · Accepted Answer

$2b = a + c$

Vedclass · Answer

(B) We know that $	an \frac{A}{2} = \sqrt{\frac{(s-b)(s-c)}{s(s-a)}}$ and $	an \frac{C}{2} = \sqrt{\frac{(s-a)(s-b)}{s(s-c)}}$.Multiplying these,we get $	an \frac{A}{2} 	an \frac{C}{2} = \sqrt{\frac{(s-b)(s-c)}{s(s-a)} \cdot \frac{(s-a)(s-b)}{s(s-c)}} = \sqrt{\frac{(s-b)^2}{s^2}} = \frac{s-b}{s}$.Given $	an \frac{A}{2} = \frac{5}{6}$ and $	an \frac{C}{2} = \frac{2}{5}$,we have $\frac{s-b}{s} = \frac{5}{6} \cdot \frac{2}{5} = \frac{1}{3}$.Thus,$3(s-b) = s$ $\Rightarrow 3s - 3b = s$ $\Rightarrow 2s = 3b$.Since $2s = a + b + c$,we have $a + b + c = 3b$,which simplifies to $a + c = 2b$.

If,in a $\triangle ABC$,$\tan \frac{A}{2} = \frac{5}{6}$ and $\tan \frac{C}{2} = \frac{2}{5}$,then $a, b, c$ are such that :

Similar Questions

The atomic numbers of elements $A$,$B$,$C$ and $D$ are $Z-1$,$Z$,$Z+1$ and $Z+2$,respectively. If $B$ is a noble gas,choose the correct statements from the following:
$(1)$ $A$ has high electron affinity
$(2)$ $C$ exists in $+2$ oxidation state
$(3)$ $D$ is an alkaline earth metal

The Biodiversity Act of India was passed by the Parliament in the year:

The $V-Q$ graph is shown below. What does the area of $\Delta OAB$ represent in this graph?

The equivalent weight of phosphoric acid $(H_3PO_4)$ in the reaction,$NaOH + H_3PO_4 \to NaH_2PO_4 + H_2O$ is

Fraunhofer lines are produced by the absorption of light in

Vedclass Test Series

Exam Paper Generator

Online Exam Module