Mathematics 2007 JAMB Past Questions - Question 49: Find the value of tan 60-tan 30/tan60+tan30

Correct Answer

B

Explanation

Tan60⁰ -tan30⁰/tan60⁰ + tan 30⁰ = √3 -√1√3/√3 + 1√3 = 2√3/4/√3 = 2/4 = 1/2To find the value of (tan 60 - tan 30) / (tan 60 + tan 30), we can use the trigonometric identity:tan(A - B) = (tan A - tan B) / (1 + tan A tan B)Using this identity, we can rewrite the expression as:(tan 60 - tan 30) / (tan 60 + tan 30) = tan(60 - 30) / (1 + tan 60 tan 30)Simplifying further:= tan 30 / (1 + tan 60 tan 30)Now, we know that tan 30 = 1/√3 and tan 60 = √3.Substituting these values into the expression:= (1/√3) / (1 + (√3)(1/√3))= (1/√3) / (1 + 1)= (1/√3) / 2= 1 / (2√3)To rationalize the denominator, we multiply the numerator and denominator by √3:= (1 / (2√3)) * (√3 / √3)= √3 / (2 * 3)= √3 / 6Therefore, the value of (tan 60 - tan 30) / (tan 60 + tan 30) is √3 / 6.