Question

Cos (2π-3x)·cos x + sin 3x·cos( 3п\2 +x)

Answer 1

Ответ:

Cos (2π-3x)·cos x + sin 3x·cos( 3п\2 +x) = cos3x ·cosx + sin3x ·sinx = cos(3x-x) = cos2x

Answer 2

It looks like you've provided a mathematical expression involving trigonometric functions. Let's break down the expression step by step:

1. Cosine of the Difference Angle Formula: Cos(2π - 3x) = Cos(2π) * Cos(3x) + Sin(2π) * Sin(3x) Since Cos(2π) = 1 and Sin(2π) = 0: Cos(2π - 3x) = Cos(3x)

2. Cosine of Sum Angle Formula: Cos(3π/2 + x) = Cos(3π/2) * Cos(x) - Sin(3π/2) * Sin(x) Since Cos(3π/2) = 0 and Sin(3π/2) = -1: Cos(3π/2 + x) = -Sin(x)

Substitute these results back into your original expression:

Cos(2π - 3x) * Cos(x) + Sin(3x) * Cos(3π/2 + x) = Cos(3x) * Cos(x) + Sin(3x) * (-Sin(x)) = Cos(3x) * Cos(x) - Sin(3x) * Sin(x)

At this point, you might recognize the right side of the expression as the cosine of the difference angle formula:

= Cos(3x - x) = Cos(2x)

So, the simplified form of the given expression is Cos(2x).