Question

Упростить sin 75°sin 15° B)0,5 С 1 Д - 05

Answer 1

75°sin=0,96
15°sin=0,3

Answer 2

To simplify the expression sin 75° * sin 15°, we can use the trigonometric identity:

sin(A) * sin(B) = (1/2) * [cos(A - B) - cos(A + B)]

In this case, A = 75° and B = 15°, so we have:

sin 75° * sin 15° = (1/2) * [cos(75° - 15°) - cos(75° + 15°)]

Now, let's calculate the values inside the brackets:

cos(75° - 15°) = cos(60°) = 1/2 (using the trigonometric value of cos(60°))

cos(75° + 15°) = cos(90°) = 0 (using the trigonometric value of cos(90°))

Now, substitute these values back into the original expression:

sin 75° * sin 15° = (1/2) * [1/2 - 0]

sin 75° * sin 15° = (1/2) * (1/2) = 1/4

So, the simplified value of sin 75° * sin 15° is 1/4. Therefore, the correct answer is B) 0.25.