What is the difference between 2 cos x and cos 2x?

Solution: 

The cosine function is one of the primary mathematical trigonometric functions. It is complementary to the cosine function (co + cosine)

2 cosx is the double of cosine function which means cos x is multiplied by 2. i.e 2 × cosx. Its range lies between [-2,2].

We know that cos x lies in the range of [-1, 1] thus, the range of 2cosx will be 2 × [-1, 1] = [-2, 2] 

Graph of 2 cosx is twice as high compared to cos x, but it is always centred around the x-axis.

cos 2x is the double of angle x which means that the angle of the function cosine is multiplied by 2. i.e cos (2 × x). Its range lies between [-1,1]

The amplitude remains the same. The angle 2x completes a cycle in half the time compared to cos x 

Graph of cos 2x has double the frequency of cos x.

Therefore, 2 cosx is twice the cosine of angle x and lies in the range of [-2 , 2] whereas, cos 2x is the cosine of the angle 2x, two times the angle x and it lies between [-1 , 1]

What is the difference between 2 cos x and cos 2x?

Summary:

2cosx is twice the cosine of angle x and lies in the range of [-2 , 2] whereas, cos 2x is the cosine of the angle 2x, two times the angle x and it lies between [-1 , 1].