Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

What is the difference between 2cosx and cos2x?

Answer
VerifiedVerified
440.1k+ views
1 likes
like imagedislike image
Hint: In the function 2cosx the cosine term is doubled, while in the function cos2x, the argument of the cosine function will get doubled. The difference between the two functions will get reflected in their ranges. The range of the cosine function, which is a sinusoidal function, is equal to [1,1]. From this range, we can obtain the ranges of both the given functions.

Complete step by step solution:
The trigonometric functions given in the above question are 2cosx and cos2x. Let us consider these trigonometric functions as
y=cos2x......(i)y=2cosx......(ii)
We can see that both the functions are expressed in terms of the cosine function. The difference between the two is in the first function, the argument is doubled, while in the second function, the cosine of the argument x is doubled.
We know that the cosine is a sinusoidal function whose value varies from 1 to 1. Therefore, the range of the function represented in the equation (i) will be equal to [1,1].
In the function represented in the equation (ii), since the cosine term, whose value varies from 1 to 1 is doubled, its range will be given by
2[1,1][2,2]
Thus, the range of the function 2cosx is equal to [2,2].
We can interpret the difference in the two functions by their graphs given below.
seo images

seo images


Note: From the graph of the two functions in the above solution we can appreciate that the difference is not only in their ranges, but their periods too. The period of the first function cos2x is half of that of the second function 2cosx. We can also show the difference between the given functions by considering the function of their difference, that is, y=cos2x2cosx. We can simplify this function using the trigonometric identity cos2x=2cos2x1 so that the function gets simplified to y=2cos2x2cosx1.