Question

СРОЧНО!cos 5Пи/12 * cos Пи/12​

Answer 1

Ответ:

Ответ находится на фотографии

Answer 2

Ответ:

0

Объяснение:

сos∝*сosβ=0.5*(cos(∝-β)+cos(∝+β))

cos 5π/12 * cosπ/12​=0.5*(cos(5π/12-π/12) + cos(5π/12+π/12))=

0.5*cos(4π/12) * cos(6π/12)=0.5*cos(π/3) * cos(π/2)=0.5*0.5*0=0

Answer 3

To evaluate the expression cos(5π/12) * cos(π/12), we can use the trigonometric identity:

cos(a - b) = cos(a) * cos(b) + sin(a) * sin(b)

Let's apply this identity:

cos(5π/12) * cos(π/12) = cos(π/3 - π/4) * cos(π/4)

Using the identity, we have:

cos(π/3 - π/4) = cos(π/3) * cos(π/4) + sin(π/3) * sin(π/4)

Recall that cos(π/3) = 1/2 and sin(π/3) = √3/2, and cos(π/4) = √2/2 and sin(π/4) = √2/2.

Plugging in these values, we get:

cos(π/3) * cos(π/4) + sin(π/3) * sin(π/4) = (1/2) * (√2/2) + (√3/2) * (√2/2)

Multiplying the fractions, we have:

(1/2) * (√2/2) + (√3/2) * (√2/2) = √2/4 + √6/4

Combining the terms, we get:

√2/4 + √6/4 = (√2 + √6) / 4

Therefore, cos(5π/12) * cos(π/12) is equal to (√2 + √6) / 4.