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One of the root equation cosx-x+1/2=0 li...

One of the root equation `cosx-x+1/2=0` lies in the interval (a)`(0,pi/2)` (b) `(-pi/(2,0))` (c) `(pi/2,pi)` (d) `(pi,(3pi)/2)`

A

`(0, pi/2)`

B

`(- pi/2, 0)`

C

`(pi/2, pi)`

D

`(pi, (3pi)/2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `f(x)=cos x-x+1/2`
`f(0)=1+1/2 gt 0`
`f(pi/2)=0- pi/2 + 1/2=(1-pi)/2 lt 0`
Therefore, one root lies in the interval `(0, pi/2)`.
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