Question

Сколько будет cos^215° - sin^215°?

Answer 1

Применим здесь формулу:
cos²x – sin²x = cos2x


cos²15° – sin²15° = cos( 2×15° ) = cos30° = √3 / 2



ОТВЕТ: √3 / 2

Answer 2

To find the value of cos^215° - sin^215°, we need to understand that "cos^215°" means "cosine of 215 degrees raised to the power of 215," and "sin^215°" means "sine of 215 degrees raised to the power of 215." These expressions are quite complex and not easy to compute directly. However, there is a trigonometric identity that can help simplify the calculation:

cos(x) - sin(x) = √2 * sin(x + 45°)

Using this identity, we can rewrite the expression:

cos^215° - sin^215° = √2 * sin(215° + 45°)

Now, let's find the value of sin(215° + 45°):

sin(215° + 45°) = sin(260°)

Since the sine function is periodic, sin(x) = sin(x + 360°), we can simplify further:

sin(260°) = sin(260° - 360°) = sin(-100°)

Now, the sine function is an odd function, meaning sin(-x) = -sin(x):

sin(-100°) = -sin(100°)

So, cos^215° - sin^215° = √2 * (-sin(100°))

Now, we need to evaluate sin(100°). Beyond this point, we can use a calculator to get a numerical approximation.

sin(100°) ≈ -0.98480775301

Therefore:

cos^215° - sin^215° ≈ √2 * (-(-0.98480775301)) ≈ √2 * 0.98480775301 ≈ 1.39305739368

So, the approximate value of cos^215° - sin^215° is 1.393. Keep in mind that this is an approximation due to rounding the value of sin(100°).