Mathematics 2007 JAMB Past Questions - Question 50: The area of a square is 144²cm.find the length of the diagonal

Correct Answer

B

Explanation

Arwa = Ssup2 = 144sq.cm there S = √144 = 12cm.Length of diagonal = √12sup2 +12sup2 = √144 +144 =√228= 12 √2cmTo 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.