Question

Cos(25)×cos(15)−sin(25)×sin(15)

Answer 1

Решение:

Вычислим по формуле косинус суммы.

$\boldsymbol{\cos(\alpha)cos(\beta)-\sin(\alpha)sin(\beta)=\cos(\alpha +\beta) \Longrightarrow}$

$\cos(25)\cos(15)-\sin(25)\sin(15)=\cos(25+15)=\underline{\cos40}$

Ответ:   $\Large { \boxed{ \bold { \cos(40)}} }$

Answer 2

To simplify the expression $\cos(25^\circ) \times \cos(15^\circ) - \sin(25^\circ) \times \sin(15^\circ)$, you can use the angle difference identity for cosine, which states:

$\cos(A - B) = \cos(A) \times \cos(B) + \sin(A) \times \sin(B).$

Comparing this with the given expression, you can see that it matches the form of the cosine of the difference of two angles. So, you can rewrite the expression as:

$\cos(25^\circ - 15^\circ).$

Now, subtract the angles:

$= \cos(10^\circ).$

So, (\cos(25^\circ) \times \cos(15^\circ) - \sin(25^\circ) \times \sin(15^\circ) = \cos(10^\circ).]