Question

How to prove that : tan 75°-tan 30°-tan75°.tan30° = 1

Answer 1

NOTE: tan(A+/-B) = (tanA +/- tanB) / (1 -/+ tanAtanB)  

tan 75 - tan 30 - tan75tan 30=1 can also be written as:  

tan 75 - tan 30 = 1 + tan75tan 30 or  

tan 75 - tan 30/1 + tan75tan 30 = 1 = tan(75-30) = tan(45) = 1  

LHS=RHS=1