If `A+B=pi/3a n dcosA+cos B=1,` then find the value of `cos((A-B)/2)dot`

Explanation

Given:



`A+B=frac{pi}{3} text { and } cos A+cos B=1 `


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


`Rightarrow 2 cos (frac{pi}{6}) cos (frac{A-B}{2})=1[because A+B=frac{pi}{3}] `


`Rightarrow 2 times frac{sqrt{3}}{2} times cos (frac{A-B}{2})=1 `


`Rightarrow cos (frac{A-B}{2})=frac{1}{sqrt{3}}`