Question

2) COs 47° ×COS 17° + Sin47° ×sin 17°​

Answer 1

Пошаговое объяснение:

Это косинус разности

$\cos(47 ^{∘} - 17^{∘} ) = \cos(30^{∘} ) = \frac{ \sqrt{3} }{2}$

Answer 2

The expression you're asking about is a trigonometric identity known as the sum-to-product identity. This identity states that `cos(A)cos(B) + sin(A)sin(B)` is equal to `cos(A-B)`. In this case, A is 47° and B is 17°.

Here's how you can solve it:

1. Substitute A and B into the sum-to-product identity: `cos(47°)cos(17°) + sin(47°)sin(17°)`. 2. Simplify the expression to `cos(47° - 17°)`. 3. The result of `cos(47° - 17°)` is `cos(30°)`. 4. Finally, find the value of `cos(30°)`. According to the table of trigonometric values, `cos(30°) = sqrt(3) / 2`.

So, the result of the expression `cos(47°)cos(17°) + sin(47°)sin(17°)` is `sqrt(3) / 2` , .