Question

/17. Using the formula, tan 2A = 2 tanA/1-tan 2 a, find the value of tan 60°, it
being given that tan 30°​

Answer 1

Question:

Using the formula, tan2A = 2•tanA/(1-tan²A) , find the value of tan 60°, it being given that ;

tan30° = 1/√3 .

Answer:

tan60° = √3

Note:

• tan@ = perpendicular / base

• tan(A+B) = (tanA + tanB)/(1 - tanA•tanB)

• tan(A-B) = (tanA - tanB)/(1 + tanA•tanB)

• tan2A = 2tanA/(1 - tan²A)

• tan0° = 0

• tan30° = 1/√3

• tan45° = 1

• tan60° = √3

• tan90° = ∞

Solution:

We know that;

tan2A = 2tanA/(1 - tan²A)

Also,

We can write 60° as 2×30° .

Thus,

=> tan60° = tan(2×30°)

=> tan60° = 2tan30°/(1 - tan²30°)

=> tan60° = [2×(1/√3)]/[1 - (1/√3)²]

=> tan60° = (2/√3)/(1 - 1/3)

=> tan60° = (2/√3)/[(3 - 1)/3]

=> tan60° = (2/√3)/(2/3)

=> tan60° = (2/√3)×(3/2)

=> tan60° = √3

Hence,

The obtained value of tan60° is √3 .