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Question

Number of integers in the range of 13tan2x1+tan2x is 


Solution

Given: 13tan2x1+tan2x
We know that,
x(2n+1)π2
Now,
13tan2x1+tan2x=1tan2x+121+tan2x=1tan2x1+tan2x+121+tan2x=cos2x+12cos2x=cos2x+6(1+cos2x)=7cos2x+6

As x(2n+1)π2, so 
cos2x(1,1]
Therefore, 
13tan2x1+tan2x(1,13]

Hence, the number of integral values in the range is 14.

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