Question

If A = 60⁰ and B = 30⁰, verify that: 

(iii) tan (A-B) = `(tan A-tanB)/(1+tan A tan B)`

Answer 1

tan (A – B) = tan 60^{0 =` 1/sqrt(3)`}

`(tan A - tan B)/(1+ tan A tan B) = (tan 60^0 - tan 30^60)/(1+tan60^0tan30^0) = (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)`