n Using the formula, tan 2A = (2tan A)/(1-tan² A), find the value of tan 60°, it begin given that tan 30° = 1/√3 ANSWERGiven : -Using the formula, tan 2A = (2tan A)/(1-tan² A) . Required to find : - value of tan 60° ? Condition mentioned : - Use the formula;tan 2A = (2tan A)/(1-tan² A)Solution : - tan 2A = (2tan A)/(1-tan² A)We need to find the value of tan 60° So,A = 30° This implies;➙ tan 2(30°) = (2tan 30°)/(1-tan² 30°) ➙ tan 60° = (2tan 30°)/(1-tan² 30°) We know that; tan 30° = 1/√3 ➙ tan 60° = (2 x 1/√3 )/(1-[1/√3]² )➙ tan 60° = (2/√3)/(1-1/3) ➙ tan 60° = (2/√3)/([3-1]/[3]) ➙ tan 60° = (2/√3)/(2/3)➙ tan 60° = (2/√3)÷(2/3)➙ tan 60° = (2/√3)x(3/2)➙ tan 60° = 2/√3 x 3/2 ➙ tan 60° = 3/√3 Here,Let's rationalize the denominator ! ➙ Rationalising factor of √3 = √3 Multiply the NUMERATOR and denominator with rationalising factor➙ tan 60° = 3/√3 x √3/√3 ➙ tan 60° = (3√3)/(√3)² ➙ tan 60° = (3√3)/(3) ➙ tan 60° = √3 Therefore,➙ Value of tan 60° = √3 Additional Information We can also find the value of tan 60° using the formula;tan (A+B) = (tan A+tan B)/(1-tan A tan BLet's find out how we can find the value of tan 60° using this formula . CONSIDER the formula; tan (A+B) = (tan A+tan B)/(1-tanA tan B)Here,A = 30° B = 30° ➙ tan (30°+30°) = (tan 30°+tan 30°)/(1-tan 30° tan 30°)➙ tan 60° = (tan 30°+tan 30°)/(1-tan 30° tan 30°)We know that; tan 30° = 1/√3 ➙ tan 60° = (1/√3+1/√3)/(1-1/√3 x 1/√3)➙ tan 60° = ([1+1]/[√3])/(1 - 1/3 )➙ tan 60° = (2/√3)/([3-1]/[3])➙ tan 60° = (2/√3)/(2/3)➙ tan 60° = (2/√3)÷(2/3)➙ tan 60° = (2/√3) x (3/2)➙ tan 60° = 3/√3Now,Let's rationalize the denominator R.F. of √3 = √3 This implies;➙ tan 60° = 3/√3 x √3/√3➙ tan 60° = (3√3)/([√3]²)➙ tan 60° = (3√3)/(3)➙ tan 60° = √3 Hence,➙ Value of tan 60° = √3