Question

(1-tg16xtg44)/(tg16+tg44)

Answer 1

Решение смотри на фотографии

Answer 2

We can simplify the given expression as follows:

(1 - tg(16) * tg(44)) / (tg(16) + tg(44))

Let's use the trigonometric identity: tg(a + b) = (tg(a) + tg(b)) / (1 - tg(a) * tg(b))

By using this identity, we can write:

tg(16 + 44) = tg(60) = sqrt(3)

tg(16) + tg(44) = tg(16 + 44) - tg(16) * tg(44) = sqrt(3) - tg(16) * tg(44)

So, the original expression becomes:

(1 - tg(16) * tg(44)) / (sqrt(3) - tg(16) * tg(44))

Now, let's simplify further by multiplying both the numerator and the denominator by the conjugate of the denominator, which is (sqrt(3) + tg(16) * tg(44)):

[(1 - tg(16) * tg(44)) / (sqrt(3) - tg(16) * tg(44))] * [(sqrt(3) + tg(16) * tg(44)) / (sqrt(3) + tg(16) * tg(44))]

= (sqrt(3) + tg(16) * tg(44) - tg(16) * tg(44) - tg^2(16) * tg^2(44)) / (3 - tg^2(16) * tg^2(44))

= (sqrt(3) - tg^2(16) * tg^2(44)) / (3 - tg^2(16) * tg^2(44))

Therefore, the simplified expression is:

(sqrt(3) - tg^2(16) * tg^2(44)) / (3 - tg^2(16) * tg^2(44))