Question

If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.

Answer 1

It is given that A = 60°, B = 30° 
Putting A = 60° and B = 30° in the given equation,
we get

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

⇒ tan( 60° - 30° ) = `(tan 60° - tan 30° )/(1 + tan 60°. tan 30° )`

⇒ tan 30° = `(sqrt3 - 1/sqrt3)/(1 + sqrt3 xx 1/sqrt3)`

⇒ `((3-1)/sqrt3)/2`

⇒ `(2/sqrt3)/(2/1)`

⇒ `2/(2sqrt3)`

⇒ `1/sqrt3`

⇒ LHS = RHS