The expression cos4x cos3x+ sin4x sin3x is equilvalent to?
To simplify the expression cos(4x)cos(3x) + sin(4x)sin(3x), we can use the trigonometric identity called the cosine of the difference of two angles, which states:
cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
In this case, we have cos(4x)cos(3x) + sin(4x)sin(3x), which matches the form of the cosine difference identity.
Therefore, the expression is equivalent to cos(4x - 3x).
Subtracting the exponents, we get cos(x).
So, the simplified expression is cos(x).
To simplify the expression cos(4x)cos(3x) + sin(4x)sin(3x), we can use the trigonometric identity:
cos(A - B) = cos(A)cos(B) + sin(A)sin(B).
Comparing this identity with our given expression, we see that A = 4x and B = 3x.
So, using the identity, we can rewrite the expression as:
cos(4x - 3x)
Now, simplifying the new expression:
cos(x)
Therefore, the equivalent expression is cos(x).