Question

Given A = 60° and B = 30°,

prove that: tan (A - B) = `(tan"A"  –  tan"B")/(1 + tan"A".tan"B")`

Answer 1

LHS = tan(A – B) 

= tan (60° – 30°)

= tan30°

= `(1)/(sqrt3)`

RHS = `(tan"A"  –  tan"B")/(1 + tan 60°. tan 30°)`

= `(tan60° –  tan30°)/(1+tan 60°.tan30°)`

= `(sqrt3  –  1/(sqrt3))/(1 + sqrt3(1/sqrt3))`

= `(2)/(2sqrt3)`

= `(1)/sqrt3`

LHS = RHS