If `cos A=m cos B ,` then write the value of `cot((A+B)/2)cos((A-B)/2)`

Explanation

Given:


`Rightarrow frac{cos A=m cos B}{cos A}=frac{m}{1}`


`Rightarrow frac{cos A+cos B}{cos A-cos B}=frac{m+1}{m-1}`


`Rightarrow frac{2 cos (frac{A-B}{2}) cos (frac{A+B}{2})}{-2 sin (frac{B+A}{2}) sin (frac{B-A}{2})}=frac{m+1}{m-1}[because cos A+cos B=2 cos (frac{A-B}{2}) cos (frac{A+B}{2}).` and `.cos A-cos B=2 sin (frac{A+B}{2}) cos (frac{B-A}{2})]`


`Rightarrow frac{cos (frac{B-A}{2}) cos (frac{A+B}{2})}{sin (frac{A+B}{2}) sin (frac{B-A}{2})}=frac{m+1}{m-1}`


`Rightarrow cot (frac{A+B}{2}) cot (frac{B-A}{2})=frac{m+1}{m-1}`