Question

Question #f387d

Answer 1

Simplest answer: Not.

Next simplest: The 4's are not factors of the numerator and denominator. You couldn't say cos(4x) = 4 cos(x) etc and then cancel 4's. Well you could but you'd be wrong.

One way to know these are different is that the graph of y = cos(4x) has frequency 4, while y = 4 cos(x) has amplitude 4.

Another approach: `cos(4x)/sin(4x) = cot(4x)` but `cos(x)/sin(x) = cot(x)` so where's the 4 now?

Thanks for reading this far, and you're welcome! \from dansmath/