Question

210. Найдите значение выражения tg 15° : tg 30° : tg 45° : tg 60° - tg 75°. Умоляю помогите это Соч .даю все балы​

Answer 1

Ответ:

g 15 · tg 30 · tg 60 · tg 75 =

= (tg 15· tg 75) · (tg 30 · tg 60) =

= (tg 15· ctg 15) · (tg 30 · ctg 30) =

= 1 · 1 = 1

Пошаговое объяснение:

Answer 2

Calculation of the Expression

To find the value of the expression tg 15° : tg 30° : tg 45° : tg 60° - tg 75°, we need to calculate the tangent of each angle and then subtract the tangent of 75° from the sum of the tangents of 15°, 30°, 45°, and 60°.

Let's calculate the tangent of each angle:

- tg 15°: The tangent of 15° is approximately 0.267949192. - tg 30°: The tangent of 30° is approximately 0.577350269. - tg 45°: The tangent of 45° is exactly 1. - tg 60°: The tangent of 60° is approximately 1.732050808. - tg 75°: We will calculate this later.

Now, let's substitute these values into the expression:

tg 15° : tg 30° : tg 45° : tg 60° - tg 75° = 0.267949192 : 0.577350269 : 1 : 1.732050808 - tg 75°

To find the value of tg 75°, we can use the identity tg 75° = 1 / tg 15°.

Let's calculate tg 75°:

tg 75° = 1 / tg 15° = 1 / 0.267949192 ≈ 3.732050808

Now, let's substitute this value back into the expression:

tg 15° : tg 30° : tg 45° : tg 60° - tg 75° = 0.267949192 : 0.577350269 : 1 : 1.732050808 - 3.732050808

Simplifying the expression further:

tg 15° : tg 30° : tg 45° : tg 60° - tg 75° = 0.267949192 : 0.577350269 : 1 : -2

Therefore, the value of the expression tg 15° : tg 30° : tg 45° : tg 60° - tg 75° is 0.267949192 : 0.577350269 : 1 : -2.

Please note that the values provided are approximate and may have slight variations due to rounding.