Question

Cos3xcosx-sin3xsinx=

Answer 1

Cos3x*cosx -sin3x*sinx =  -1/2 ;
cos(3x+x) = -1/2 ;
cos4x = -1/2 ; 
4x = +,- 2π/3 +2πn ,n∈Z.
x = +,- π/6 +(π/2)*n ,n∈Z.

Answer 2

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

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

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

Now, we can use the sum and difference identities for cosine to simplify the expression:

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

So, the simplified expression is:

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