Question

Cos24 + cos48 - cos84 - cos12=1/2

Answer 1

Ответ:

нет

ответ будет 0.5

потому что левая и правая часть разные

Answer 2

The equation you provided is a trigonometric identity involving cosine values. Let's break down the equation step by step to verify if it holds true:

cos(24°) + cos(48°) - cos(84°) - cos(12°) = 1/2

Using trigonometric identities and properties, we can manipulate the equation to verify its validity:

1. Apply the sum-to-product identity for cosine: cos(A) + cos(B) = 2 * cos((A + B) / 2) * cos((A - B) / 2)

2. Apply the identity for cos(2A): cos(2A) = 2 * cos^2(A) - 1

3. Apply the identity for cos(3A): cos(3A) = 4 * cos^3(A) - 3 * cos(A)

Let's apply these identities step by step:

cos(24°) + cos(48°) - cos(84°) - cos(12°)

= 2 * cos((24° + 48°) / 2) * cos((48° - 24°) / 2) - 2 * cos((84° + 12°) / 2) * cos((84° - 12°) / 2) = 2 * cos(36°) * cos(12°) - 2 * cos(48°) * cos(36°)

Now we can use the identity for cos(2A) on the first term: = 2 * (2 * cos^2(18°) - 1) * cos(12°) - 2 * cos(48°) * cos(36°) = 4 * cos^2(18°) * cos(12°) - 2 * cos(12°) - 2 * cos(48°) * cos(36°)

Now we can use the identity for cos(3A) on the second term: = 4 * cos^2(18°) * cos(12°) - 2 * cos(12°) - 2 * (4 * cos^3(12°) - 3 * cos(12°)) * cos(36°) = 4 * cos^2(18°) * cos(12°) - 2 * cos(12°) - 8 * cos^3(12°) * cos(36°) + 6 * cos(12°) * cos(36°)

At this point, the equation becomes more complicated, and it's not clear if the equation will simplify to 1/2. Simplifying further might be complex, and it's possible that the equation doesn't simplify exactly to 1/2.

Please double-check the equation or provide additional context if needed. If you have access to a calculator or a symbolic algebra system, you might be able to evaluate the expression more accurately.