Question

Cos8x cos4x + sin8x sin4x=​

Answer 1

Ответ:

x=±π/12+1/2πn, n∈Z

Объяснение:

cos8x cos4x + sin8x sin4x=1/2

cos(8x-4x)=1/2

cos4x=1/2

4x=+-pi/3+2pin

x=±π/12+1/2πn, n∈Z

Answer 2

The given expression can be simplified using the trigonometric identity:

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

Let's apply this identity to the given expression:

cos(8x) cos(4x) + sin(8x) sin(4x) = cos(8x - 4x)

Simplifying further:

cos(8x - 4x) = cos(4x)

Therefore, the simplified expression is:

cos(4x)