ISI objective question 650

[Lakshmi]

The equation 2x=(2n+1) pi (1-cosx), where n is any positive integer, has

a) infinitely many roots

b)exactly 2n+1 roots

c)exactly one root

d)exactly 2n+3 roots

Ive seen the solution using graphs. Is there any other way to solve this?

[Shreya Nair]

First rearrange the equation as cosx= -2x/(2n+1)π+ 1. Now consider any value of n, say, n=2 and then just draw graphs of y=cosx and y= -2x/(2n+1)π +1. You'll observe there are 5 intersection points,i.e., 2n+1 solutions

Such questions can only be solved by drawing graphs.

Hope it helps!!

[Author]

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