Question

(sin36+cos36)\(cos18-sin18)

Answer 1

Відповідь:

Пояснення:

(Sin36+cos36)/(cos18-sin18)=(0,58778+0,80901)/(0,95105-0,30901)= 1,39679/0,64204=2,17554981

Answer 2

Let's simplify the expression step by step:

1. sin(36) + cos(36): We know that sin(36°) = cos(54°) and cos(36°) = sin(54°) due to their complementary angles relationship.

   So, sin(36°) + cos(36°) = cos(54°) + sin(54°).

2. cos(18) - sin(18): We can use the same logic here since cos(18°) = sin(72°) and sin(18°) = cos(72°) due to their complementary angles relationship.

   Therefore, cos(18°) - sin(18°) = sin(72°) - cos(72°).

Now, let's substitute these values back into the original expression:

(sin(36°) + cos(36°)) / (cos(18°) - sin(18°)) = (cos(54°) + sin(54°)) / (sin(72°) - cos(72°)).

At this point, we might not be able to simplify this further without using numerical approximations because the angles involved (54° and 72°) are not standard angles for which we have exact trigonometric values.

If you're looking for a numerical approximation, you could use a calculator to find the decimal value of the expression. Keep in mind that the resulting value might not be a simple or neat number due to the combination of trigonometric functions involved.