Question

Cos 5pi/12+cos pi/12

Answer 1

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Используем формулу суммы косинусов:
cosa + cosb = 2× cos( (a+b)/2 ) × cos( (a-b)/2 )
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cos( 5π/12 ) + cos( π/12 ) = 2 × cos( (5π/12 + π/12) ÷2 ) × cos( (5π/12 - π/12) ÷ 2 ) = 2 × cos( π/4 ) × cos( π/6 ) = 2 × √2/2 × √3/2 = √6/2

Ответ: √6/2

Answer 2

Ответ на картинке внизу

Answer 3

To simplify the expression, we can use the trigonometric identity:

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

Let's apply this identity to the given expression:

cos(5π/12) + cos(π/12) = cos(4π/12 + π/12) + cos(π/12)

Now, we can rewrite 4π/12 as π/3:

cos(π/3 + π/12) + cos(π/12)

Now we can apply the identity:

cos(π/3) * cos(π/12) - sin(π/3) * sin(π/12) + cos(π/12)

Since cos(π/3) = 1/2 and sin(π/3) = √3/2, we can substitute these values:

(1/2) * cos(π/12) - (√3/2) * sin(π/12) + cos(π/12)

Now we have two terms involving cos(π/12), so we can combine them:

(1/2 + 1) * cos(π/12) - (√3/2) * sin(π/12)

Simplifying further:

(3/2) * cos(π/12) - (√3/2) * sin(π/12)

Unfortunately, we can't simplify this expression further without knowing the exact value of cos(π/12) and sin(π/12). If you have the specific numerical values of these trigonometric functions, you can substitute them in the expression to get a numeric answer.