Question

Вычислить 4cos75!подробный метод решения пожалуйста

Answer 1

4cos*(30 градусов + 45 градусов) =4cos*30 градусов *cos 45 градусов - 4sin 30 градусов * sin 45 градусов =(корень из 6) - (корень из 2).
вот так)

Answer 2

To calculate the value of 4cos75, we can use the trigonometric identity:

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

In this case, we can rewrite 4cos75 as 4cos(45 + 30). Using the above identity, we have:

4cos(45 + 30) = 4(cos45cos30 - sin45sin30)

Now, let's calculate the values of cos45, cos30, sin45, and sin30:

- cos45 = √2/2 - cos30 = √3/2 - sin45 = √2/2 - sin30 = 1/2

Substituting these values into the equation, we get:

4(cos45cos30 - sin45sin30) = 4(√2/2 * √3/2 - √2/2 * 1/2)

Simplifying further:

4(√6/4 - √2/4) = √6 - √2

Therefore, the value of 4cos75 is √6 - √2.

Please let me know if you need any further clarification or assistance!