Question

cos4x*cos3x + sin4x*sin3x

Answer 1

= cos(4x-3x)

= cos (x) by applying the cos(A-B) expansion

Answer 2

Cos x

Answer 3

[AI-generated answer — Explain Bot]

To simplify the expression cos(4x) * cos(3x) + sin(4x) * sin(3x), we can use the trigonometric identity known as the angle sum formula, which states:

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

We notice that the expression given is similar to the right-hand side of the angle sum formula. By comparing the given expression with the formula, we can see that a = 4x and b = 3x.

So, substituting these values into the angle sum formula, we get:

cos(4x - 3x) = cos(4x) * cos(3x) + sin(4x) * sin(3x)

cos(x) = cos(4x) * cos(3x) + sin(4x) * sin(3x)

Therefore, the simplified expression is cos(x).

Thus, cos(4x) * cos(3x) + sin(4x) * sin(3x) simplifies to cos(x).