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Question

If tan2x5secx=1 for exactly 7 distinct values of x[0,nπ2],nN then the greatest value of n is

A
13
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B
17
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C
19
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D
15
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Solution

The correct option is D 15
sexx=3cosx=13[0,2π],(2π,4π],(4π,6π]
Which gives two values of x in each of [0,2π],(2π,4π],(4π,6π] and one value in 6π+3π2=15π2
greatest value of n = 15

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