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# 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 - tan^{3} A) / (1 - 3 tan^{2} 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 tan^{2}A - √3 + 3 tan A - √3 tan^{2} A + tanA) / (1 - 3 tan^{2} A)

= tan A + (8 tan A) / (1 - 3 tan^{2} A)

= (tan A - 3tan^{3} A + 8 tan A) / (1 - 3tan^{2} A)

= 3 (3 tan A - tan^{3} A) / (1 - 3tan^{2} A)

= 3 tan(3A)

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

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