Question

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

Answer 1

tan (A – B) = tan 60°

= `1/sqrt(3)`

`(tan A - tan B)/(1 + tan A tan B) = (tan 60^circ -  tan 30^circ)/(1 + tan60^circ tan30^circ)`

= `(sqrt(3) - (1/sqrt(3)))/(1 + (sqrt(3) xx1/sqrt(3))`

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

= `3/sqrt(3)`

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