Question

If A = B = 60°, verify that: tan(A - B) = `(tan"A" - tan"B")/(1 + tan"A" tan"B"")`

Answer 1

tan(A - B) = `(tan"A" - tan"B")/(1 + tan"A" tan"B"")`

L.H.S. :
tan(A - B) = tan(60° - 60°) - tan0° = 0
R.H.S. :

`(tan"A" - tan"B")/(1 + tan"A" tan"B"")`

= `(tan 60° - tan60°)/(1 + tan60° tan60°)`

= `(sqrt(3) - sqrt(3))/(1 + sqrt(3) xx sqrt(3)`
= 0
L.H.S = R.H.S.
Therefore,
tan(A - B) = `(tan"A" - tan"B")/(1 + tan"A" tan"B"")`.