Question

If A = 30° and B = 60°, verify that: `(sin("A" -"B"))/(sin"A" . sin"B")` = cotB - cotA

Answer 1

A = 30° and B = 60°
L.H.S.
= `(sin("A" -"B"))/(sin"A" . sin"B")` 

= `(sin(30° - 60°))/(sin30° xx sin60°)`

= `(-sin"30°)/(sin30° xx sin60°)`

= `(-(1)/(2))/((1)/(2) xx sqrt(3)/(2)`

= `-(2)/sqrt(3)`
R.H.S.
= cotB - cotA
= cot60° - cot30°

= `(1)/sqrt(3) - sqrt(3)`

= `(1 - 3)/sqrt(3)`

= `-(2)/sqrt(3)`

⇒ `(sin("A" -"B"))/(sin"A" . sin"B")` = cotB - cotA.