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Question

If 2tan2x5secx=1 for exactly seven distinct values of xϵ[0,nπ2],nϵN, then find the greatest value of n.

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Solution

Given,

2tan2x5secx=1

2(sec2x1)5secx=1

2sec2x25secx=1

2sec2x5secx3=0

2secx(secx3)+1(secx3)=0

(2secx+1)(secx3)=0

secx=12,secx=3

=6π+π2=13π2

nπ2=13π2

n=13

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