Question

((Tg^2 7п/24 -tg^2 п/24):(1-tg^2 7п/24 * tg^2 а/24))^2

Answer 1

Ответ:

= 3

Пошаговое объяснение:

Answer 2

Before we begin, let's simplify the expression a bit by using trigonometric identities:

• tan(π/4) = 1
• tan(π/6) = √3/3

Using these identities, we can simplify the expression as follows:

(tan^2(7π/24) - tan^2(π/24)) / (1 - tan^2(7π/24) * tan^2(α/24))^2

Now let's simplify the denominator by using the identity:

1 - tan^2(x) = sec^2(x)

Using this identity, we get:

(sec^2(7π/24) * sec^2(α/24) - tan^2(7π/24) * tan^2(α/24)) / sec^4(7π/24) * sec^4(α/24)

Next, we can simplify the numerator by using the identity:

sec^2(x) - tan^2(x) = 1

Using this identity, we get:

(sec^2(7π/24) - tan^2(7π/24)) * (sec^2(α/24) - tan^2(α/24)) / sec^4(7π/24) * sec^4(α/24)

Now we can simplify further by using the identity:

1 + tan^2(x) = sec^2(x)

Using this identity twice, we get:

(1 + tan^2(π/24 - 7π/24)) * (1 + tan^2(π/24 - α/24)) / (1 + tan^2(7π/24)) ^2 * (1 + tan^2(α/24)) ^2

Simplifying further, we get:

(1 + tan^2(5π/24)) * (1 + tan^2(π/24 - α/24)) / (1 + 3*tan^2(π/24)) ^2 * (1 + tan^2(α/24)) ^2

Finally, using the identity:

tan(π/3 - x) = sqrt(3) * (tan(x) - sqrt(3)) / (1 + sqrt(3) * tan(x))

We can simplify the expression further to:

(4 - 3sqrt(3) * tan(π/24 - α/24)) / (13 - 9sqrt(3)) ^2