Question

2 tg 75° / 1 - tg ^2 a

Answer 1

Формула тангенса двойного угла...

Answer 2

To simplify the expression 2tg(75°) / (1 - tg^2(a)), let's first calculate the values of the trigonometric functions involved.

tg(75°) can be calculated using the tangent addition formula:

tg(75°) = tg(45° + 30°) = (tg(45°) + tg(30°)) / (1 - tg(45°) * tg(30°))

We know that tg(45°) = 1 and tg(30°) = 1/√3.

Now, let's calculate tg(75°):

tg(75°) = (1 + 1/√3) / (1 - 1 * 1/√3) = (1 + 1/√3) / (1 - 1/√3) = [(√3 + 1) / √3] / [(√3 - 1) / √3] (To rationalize the denominator, multiply the numerator and denominator by √3) = (√3 + 1) / (√3 - 1) = (√3 + 1)(√3 + 1) / (√3 - 1)(√3 + 1) (To rationalize the numerator, multiply the numerator and denominator by (√3 + 1)) = (3 + 2√3 + 1) / (3 - 1) = (4 + 2√3).

So, tg(75°) is equal to 4 + 2√3.

Now, let's calculate tg^2(a):

tg^2(a) = (tg(a))^2

Now, the given expression is 2tg(75°) / (1 - tg^2(a)), which becomes:

2(4 + 2√3) / (1 - tg^2(a)).

We still need the value of tg^2(a) to proceed further. If you have the value of tg(a), please provide it, and I can help you simplify the expression further.