Choose the correct option. tan A+ tan (60°+ A) -tan (60°- A) is equal to?

(1) 3 tan(3A)  (2) 3 tan(3A)  (3) cot(3A)  (4) sin(3A)

We can make use of trigonometric formulas to simplify expressions with complex trigonometric terms.

Answer: The value of the expression comes out to be 3 tan(3 A)

Go through the steps to find the exact value.

Explanation:

Given expression: tan A + tan (60° +  A) - tan (60° -  A)

On simplifying the given expression using the formula tan (x + y) = (tan x + tan y) / (1 - tan x tan y) and tan(3 A) = (3tan A - tan³ A) /  (1 - 3 tan² A)

tan A + tan (60° + A) - tan (60° - A)

= tan A + (tan 60° + tan A) / (1 - tan 60° tan A) - (tan 60° - tan A) / (1 + tan 60° tan A)

= tan A  + (√3 + tan A) / (1 - √3 tan A) - (√3 - tanA) / (1 + √3 tan A)

= tan A + (√3 + 3 tan A + tan A + √3 tan²A - √3 + 3 tan A - √3 tan² A + tanA) / (1 - 3 tan² A)

= tan A + (8 tan A) / (1 - 3 tan² A) 

= (tan A - 3tan³ A + 8 tan A) / (1 - 3tan² A)

= 3 (3 tan A - tan³ A) /  (1 - 3tan² A)

= 3 tan(3A)

Thus, the value of the expression comes out to be 3 tan(3A).