Question

16cos10°×cos20°×cos40°​

Answer 1

Ответ:(16sin10 * cos 10 * cos 20 * cos 40 * cos 60) / cos 10 = (8 * 2sin10 * cos 10 * cos 20 * cos 40 * cos 60) / cos 10 = (8sin 20 * cos 20 * cos 40 * cos 60) / cos 10 = (4 * 2sin20 * cos 20 * cos 40 * cos 60) / cos 10 = (4sin 40 * cos 40 * cos 60) / cos 10 = (2sin80 * cos 60) / cos 10 = (2sin 80 * 0.5) / cos 10 = sin 80 / cos 10

sin(90 - 10) / cos 10 = cos 10 / cos 10 = 1

Объяснение:

Answer 2

To calculate the value of 16cos(10°) × cos(20°) × cos(40°), you can use the trigonometric identity called the product-to-sum formula, which is given by:

cos(A) * cos(B) = 0.5 * [cos(A + B) + cos(A - B)]

Let's apply this formula step by step:

1. 16cos(10°) × cos(20°) = 0.5 * [16 * (cos(10° + 20°) + cos(10° - 20°))]

2. 16cos(10°) × cos(20°) × cos(40°) = 0.5 * [16 * (cos(30°) + cos(-10°)) * cos(40°)]

3. Since cos(30°) = √3/2 and cos(-10°) = cos(10°), we can substitute these values in:

0.5 * [16 * (√3/2 + cos(10°)) * cos(40°)]

Now, you can calculate the value:

0.5 * [16 * (√3/2 + cos(10°)) * cos(40°)]

0.5 * [16 * (√3/2 + 0.9848) * 0.7660]

0.5 * [16 * (0.8660 + 0.9848) * 0.7660]

0.5 * [16 * 1.8508 * 0.7660]

0.5 * 23.6128

The final result is approximately:

11.8064