Question

Cos(40)cos(20)-sin(40)sin(20)

Answer 1

По тригонометрическому свойству:
$cos(\alpha + \beta)=cos\alpha \cdot cos\beta - sin\alpha \cdot sin\beta$
$cos40^{\circ} \cdot cos20^{\circ}-sin40^{\circ} \cdot sin20^{\circ} = cos(40^{\circ}+20^{\circ})=cos60^{\circ}= \frac{1}{2}$

Answer 2

To simplify the expression cos(40)cos(20) - sin(40)sin(20), we can use the trigonometric identity for the cosine of the difference of two angles:

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

Let A = 40 and B = 20. Then, we have:

cos(40 - 20) = cos(40)cos(20) + sin(40)sin(20)

Now, we can evaluate cos(40 - 20):

cos(40 - 20) = cos(20)

So the simplified expression is:

cos(40)cos(20) - sin(40)sin(20) = cos(20)