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Question

The number of solutions of tan2xsec8x+1=0 in (0,12) is:

A
0
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B
1
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C
2
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D
3
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Solution

The correct option is D 3
The equation is tan2xsec8x+1=0
Now,
tan2x=sec2xl
On substituting
sec2xlsec8x+1=0
sec2x(1sec6x)=0
sec6x=1
(sec3x)2=1
secx=±1
Solutions are π,2π,3π
0 is not included in the range and
4π>12
Therefore there are only 3 solutions

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