R S Aggarwal Solutions for Exercise 1: EXERCISE 1

In a $∆ABC,\frac{a-b}{a+b}=?$

In a $∆ABC,c{\cos }^2\frac{A}{2}+a{\cos }^2\frac{C}{2}=?$

In a $∆ABC,\frac{(b-c)}{a}{\cos }^2\frac{A}{2}+\frac{(c-a)}{b}{\cos }^2\frac{B}{2}+\frac{(a-b)}{c}·{\cos }^2\frac{C}{2}=?$

In a $\Delta ABC,\Delta \left(\cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}\right)=?$

In a $∆ABC,bc{\cos }^2\frac{A}{2}+ca{\cos }^2\frac{B}{2}+ab{\cos }^2\frac{C}{2}=?$

In a $∆ABC,2abc\cos \frac{A}{2}\cos \frac{B}{2}\cos \frac{C}{2}=?$

In a $∆ABC, \mathrm{if} \cos \frac{A}{2}=\sqrt{\frac{b+c}{2c}}$, then 

In a $∆ABC, \mathrm{if} \cot \frac{A}{2}:\cot \frac{B}{2}:\cot \frac{C}{2}=3:5:7, \mathrm{then} a:b:c=?$