Question

Sin15°cos7°-cos79°cos11°​

Answer 1

Ответ: 0,5sin8°

Объяснение:

sin15°cos7°-cos79°cos11°​ =0,5(sin22°+sin8° ) - cos(90° -11°)cos11 =

0,5 (sin22° +sin8°) - sin11°cos11° =  0,5(sin22° +sin8°)  - 0,5 (sin22°) =0,5sin8°.

Answer 2

Ответ:

0,881175

Объяснение:

Answer 3

To simplify the expression sin(15°)cos(7°) - cos(79°)cos(11°), we can use trigonometric identities to rewrite the angles in terms of their complements or differences. Here's how you can do it step by step:

1. Use the angle sum identity for sine: sin(A - B) = sin(A)cos(B) - cos(A)sin(B).
2. Use the angle sum identity for cosine: cos(A - B) = cos(A)cos(B) + sin(A)sin(B).
3. Use the fact that the cosine of a complement is the sine of the angle: cos(90° - A) = sin(A).
4. Use the fact that the sine of a complement is the cosine of the angle: sin(90° - A) = cos(A).

Let's apply these steps to the expression:

sin(15°)cos(7°) - cos(79°)cos(11°)

Step 1: sin(15°)cos(7°) - cos(79°)cos(11°) = (sin(15°)cos(7°)) - (cos(79°)cos(11°))

Step 2: = sin(15° - 7°) - cos(79° + 11°) = sin(8°) - cos(90°) = sin(8°) - 0 = sin(8°)

So, the simplified expression is sin(8°).