How do I write cos(11x)cos(x)+sin(11x)sin(x) as a single trigonometric function? Please show steps.
recall that
cos(a-b) = cosa cosb - sina sinb
To simplify the expression cos(11x)cos(x) + sin(11x)sin(x) as a single trigonometric function, we can use the identity cos(A - B) = cos(A)cos(B) + sin(A)sin(B).
Let's rewrite the given expression: cos(11x)cos(x) + sin(11x)sin(x)
Using the identity stated above, we can simplify it as follows:
cos(11x)cos(x) + sin(11x)sin(x) = cos(11x - x)
Simplifying the argument inside the cosine function, we have:
11x - x = 10x
Now, substituting this back into the expression, we get:
cos(11x)cos(x) + sin(11x)sin(x) = cos(10x)
Therefore, the given expression can be simplified as cos(10x).