If `2tan^2x-5secx=1`
for exactly seven distinct value of `x in [0,(npi)/2],n in N`
then find the greatest value of `ndot`
Text Solution
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`2 tan^(2)x-5 sec x=1` or `2 sec^(2)x-2-5 sec x=1` or `2 sec^(2) x-5 sec x-3 =0` or `sec x=3" "( :' sec x= -1/2" not possible")` This gives two values of x in each of `[0, 2pi], (2pi, 4pi], (4pi, 6pi]` and one value in `(6pi, 6 pi +(3pi)/2]` for n to be greatest. `:.` Greatest value of `n=15`
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