Question

Срочно пожалуйста! вычислить по формуле сложения cos П/7 cos 4П/21-sin П/7 sin 4П/21???

Answer 1

Решение дано на фото.

Answer 2

Calculating the Expression

To calculate the expression cos(π/7) * cos(4π/21) - sin(π/7) * sin(4π/21), we can use the trigonometric identity for the difference of two angles:

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

We can rewrite the given expression using this identity.

Applying the Trigonometric Identity

Using the identity cos(A - B) = cos(A) * cos(B) + sin(A) * sin(B), we can rewrite the given expression as:

cos(π/7) * cos(4π/21) - sin(π/7) * sin(4π/21) = cos(π/7 - 4π/21)

Simplifying the Expression

Now, we can simplify the expression by finding the difference of the angles inside the cosine function:

π/7 - 4π/21 = (3π/21) - (4π/21) = -π/21

So, the expression simplifies to:

cos(-π/21)

Calculating the Final Value

Using the property that cos(-x) = cos(x), we can further simplify the expression to:

cos(π/21)

Final Result

Therefore, the value of the given expression cos(π/7) * cos(4π/21) - sin(π/7) * sin(4π/21) is cos(π/21).

I hope this helps! If you have any other questions or need further assistance, feel free to ask.