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The number of solutions of the equation ...

The number of solutions of the equation `tanx+secx=2cosx` lying in the interval `[0,2pi]` is

A

2

B

1

C

0

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `tanx+secx=2cosx`
`rArr(sinx)/(cosx)+(1)/(cosx)=2cosx`
`rArrsinx+1=2cos^(2)x`
`rArr1+sinx=2-2sin^(2)x,cosxne0`
`rArr2sin^(2)x+sinx-1=0`
`rArr(2sinx-1)(sinx+1)=0rArrsinx=-1,(1)/(2)`
`rArrx=(pi)/(6),(5pi)/(6),(3pi)/(2) " " [becausex in(0,2pi)]`
But at `x=(3pi)/(2)` given equation does not exits.
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