Question

Cos20+cos40 cos75-cos15

Answer 1

Cos60=одна вторая

cos60= одна вторая

Answer 2

To simplify the expression, let's use the trigonometric identity:

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

We can rewrite the expression as follows:

cos(20) + cos(40) * (cos(75) - cos(15))

Using the identity, we can expand the expression:

cos(20) + cos(40) * (cos(75) - cos(15)) = cos(20) + cos(40) * (cos(45 + 30) - cos(45 - 30)) = cos(20) + cos(40) * (cos(45)cos(30) - sin(45)sin(30) - cos(45)cos(30) + sin(45)sin(30)) = cos(20) + cos(40) * (sqrt(2)/2 * sqrt(3)/2 - sqrt(2)/2 * sqrt(3)/2 - sqrt(2)/2 * sqrt(3)/2 + sqrt(2)/2 * sqrt(3)/2) = cos(20) + cos(40) * (0) = cos(20)

Therefore, the simplified expression is just cos(20).