Question

Cos 72 cos 42 + sin 72 sin 42

Answer 1

= cos(72-42)=cos30=sqrt(3)/2
sqrt = квадратный корень

Answer 2

The expression you've provided is equivalent to the cosine of the difference between 72 degrees and 42 degrees, which 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:

cos(72° - 42°) = cos(30°)

Now, you can find the exact value of cos(30°).

cos(30°) = √3/2

So, the value of the expression is:

cos(72°)cos(42°) + sin(72°)sin(42°) = (√3/2)cos(42°) + (1/2)sin(42°)

You may need to use a calculator or additional trigonometric identities to find the values of cos(42°) and sin(42°) if needed.