`(sqrt(sinA)-sqrt(sinB))/(sqrt(sinA)+sqrt(sinB)) = (a+b-2sqrt(ab))/(a-b)`

Explanation

We know that by the sine rule , `a/sin A = b/sin B = c/sin C = k `

`sin A = a/k, sin B = b/k, sin C = c/k`

Now, the LHS is

`(sqrtsinA−sqrtsinB)/(sqrtsinA+sqrtsinB)`

let us multiply and divide the above expression by `(sqrtsinA−sqrtsinB)/(sqrtsinA-sqrtsinB)`

So,`[(sqrtsinA−sqrtsinB)xx(sqrtsinA−sqrtsinB)]/[(sqrtsinA+sqrtsinB)xx(sqrtsinA−sqrtsinB)]`

=`[(sqrtsinA−sqrtsinB)^2]/[(sqrtsinA)^2−(sqrtsinB)^2]`

=`[sinA+sinB-2sqrt(sinAsinB)]/(sinA-sinB)`

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