Question

Cos19°30'cos25°30' - sin 19°30'sin25°30'

Answer 1

$cos19^{\circ }30'cos25^{\circ }30'-sin19^{\circ }30' sin25^{\circ}30'=\\\\=cos(19^{\circ }30'+25^{\circ}30')=cos45^{\circ }=\frac{\sqrt2}{2}$

Answer 2

To calculate the value of cos(19°30') * cos(25°30') - sin(19°30') * sin(25°30'), you can use the trigonometric identity for the difference of angles:

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

In this case, A = 19°30' and B = 25°30'. So, you can rewrite the expression as:

cos(19°30' - 25°30')

Now, subtract the angles:

19°30' - 25°30' = -6°

So, you have:

cos(-6°)

The cosine of -6 degrees is equal to the cosine of its positive counterpart (6 degrees), as the cosine function is even. Therefore:

cos(-6°) = cos(6°)

Now, you can calculate the value of cos(6°):

cos(6°) ≈ 0.9945

So, cos(19°30') * cos(25°30') - sin(19°30') * sin(25°30') ≈ 0.9945.