Question

Обчислити: sin75° *sin15°А) 1/2Б) 2/3В) 1/4Г) 3/8​

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To calculate sin(75°) * sin(15°), you can use the trigonometric identity:

sin(A + B) = sin(A) * cos(B) + cos(A) * sin(B)

In this case, A = 75° and B = 15°, so the identity becomes:

sin(75° + 15°) = sin(75°) * cos(15°) + cos(75°) * sin(15°)

Now, we know that sin(75°) = sin(180° - 75°) = sin(105°) and cos(75°) = -cos(180° - 75°) = -cos(105°).

So, the equation becomes:

sin(75° + 15°) = sin(105°) * cos(15°) - cos(105°) * sin(15°)

Now, we can use the following trigonometric values:

sin(15°) = 1/4 (approximated) cos(15°) = √6 - √2 / 4 (approximated)

sin(105°) = sin(180° - 105°) = sin(75°) cos(105°) = -cos(75°)

Now, substitute the values:

sin(75° + 15°) = sin(75°) * (√6 - √2) / 4 - cos(75°) * 1/4

We can rewrite sin(75°) as cos(15°) since they are complementary angles:

sin(75° + 15°) = cos(15°) * (√6 - √2) / 4 - cos(15°) * 1/4

Factor out cos(15°):

sin(75° + 15°) = cos(15°) * ((√6 - √2) / 4 - 1/4)

Now, substitute the values:

sin(75° + 15°) = (√6 - √2) / 4 - 1/4

To simplify, find a common denominator:

sin(75° + 15°) = (√6 - √2 - 1) / 4

Therefore, sin(75°) * sin(15°) = (√6 - √2 - 1) / 4.

None of the given options (A) 1/2, (B) 2/3, (C) 1/4, (D) 3/8) matches the result we obtained, so the correct answer is not among the provided choices.