Question

1. co s 70°co s 40° + si n 70°si n 40°​

Answer 1

Cos 70’cos 40’ + sin 70’sin 40’ = cos (70’ - 40’) = cos 30’ = (корень из 3)/2
Ответ: (корень из 3)/2.

Answer 2

The expression you've provided seems to be a trigonometric identity involving the sum of two trigonometric functions. Let's break it down:

1. cos(70°)cos(40°) + sin(70°)sin(40°)

This expression can be simplified using the trigonometric identity for the cosine of the difference of two angles:

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

In your case, A = 70° and B = 40°. So, the expression becomes:

cos(70° - 40°)

Now, let's calculate this:

cos(70° - 40°) = cos(30°)

The cosine of 30° is √3/2.

So, the simplified expression is:

√3/2

Therefore, cos(70°)cos(40°) + sin(70°)sin(40°) simplifies to √3/2.