Question

Sin32° Cos28°-Sin17° Cos13°

Answer 1

Ответ:

Объяснение:

Формулы тригонометрии

Answer 2

The expression you've provided seems to be a mathematical calculation involving trigonometric functions. To simplify it, we can use trigonometric identities and the properties of sine and cosine functions.

Let's break down the expression step by step:

1. Recall that the product-to-sum identity is given by:

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   Sin(A) Cos(B) = 0.5 * [Sin(A + B) + Sin(A - B)]
   

2. Applying the identity to the given expression:

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   Sin(32°) Cos(28°) - Sin(17°) Cos(13°)
   = 0.5 * [Sin(32° + 28°) + Sin(32° - 28°)] - 0.5 * [Sin(17° + 13°) + Sin(17° - 13°)]
   

3. Simplifying the angles inside the sine functions:

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   = 0.5 * [Sin(60°) + Sin(4°)] - 0.5 * [Sin(30°) + Sin(4°)]
   

4. Now, let's evaluate the sines of the angles involved:

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   Sin(60°) = √3 / 2
   Sin(30°) = 0.5
   Sin(4°) is approximately 0.069756474
   

5. Plugging in the values:

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   = 0.5 * [√3 / 2 + 0.069756474] - 0.5 * [0.5 + 0.069756474]
   = 0.5 * [0.5√3 + 0.069756474] - 0.5 * [0.569756474]
   

6. Calculating the values in the brackets:

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   = 0.25√3 + 0.034878237 - 0.284878237
   = 0.25√3 - 0.25√3
   = 0
   

So, the simplified value of the given expression is 0.