Question

Cos37 Cos53-Sin37 Sin53​

Answer 1

Объяснение:

$cos37^0cos53^0-sin37^0sin53^0=\\=\frac{1}{2}*(cos(37^0-53^0)+cos(37^0+53^0))-\frac{1}{2}*(cos(37^0-53^0)-cos(37^0+53^0))=\\=\frac{1}{2}*(cos(-16^0)+cos90^0-cos(-16^0)+cos90^0)=\frac{1}{2}*2*cos90^0=cos90^0=0.$

Answer 2

To calculate the value of the expression cos(37°) * cos(53°) - sin(37°) * sin(53°), we can use the trigonometric identity for the difference of two angles:

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

In this case, A = 37° and B = 53°. So, we can rewrite the expression as:

cos(37°) * cos(53°) - sin(37°) * sin(53°) = cos(37° - 53°)

Using the trigonometric identity above, we can substitute the values of A and B:

cos(37° - 53°) = cos(-16°)

Since the cosine function is an even function (cos(-x) = cos(x)), we can rewrite it as:

cos(-16°) = cos(16°)

Now, we can use a calculator or trigonometric tables to find the value of cos(16°).