Question

Преобразуйте произведение сos2a+cos14a+cos6a+cos10a

Answer 1

1)По формуле суммы косинусов 2*сos8x*cos6x + 2*cos8x*cos2x
2)Вынесем общий множитель 2*cos8x*(cos6x+cos2x)
3)По формуле суммы косинусов 4*cos8x*cos4x*cos2x 

Answer 2

Transformation of Trigonometric Expression

To transform the given trigonometric expression cos(2a)cos(14a)cos(6a)cos(10a), we can use the product-to-sum trigonometric identities. These identities allow us to express the product of trigonometric functions as a sum of trigonometric functions.

The product-to-sum identities are as follows: 1. cos(A)cos(B) = 0.5[cos(A+B) + cos(A-B)] 2. sin(A)sin(B) = 0.5[cos(A-B) - cos(A+B)]

We can use these identities to transform the given expression.

Transformation Steps

1. cos(2a)cos(14a) = 0.5[cos(16a) + cos(-12a)] 2. cos(6a)cos(10a) = 0.5[cos(16a) + cos(-4a)]

By applying the product-to-sum identities, we have transformed the given expression into a sum of trigonometric functions.

Final Transformed Expression

The transformed expression is: 0.5[cos(16a) + cos(-12a)] + 0.5[cos(16a) + cos(-4a)]

This is the final transformation of the given trigonometric expression using the product-to-sum trigonometric identities.