Which of the following statements about `tan10^(@)` is true?

Options

A. It is a rational number
B. It is an inrrational number less than 2
C. It is an irrational number greater than 2
D. It is greater than 2

Answer

B

Explanation

Since tan `theta` is an increasing function on `(0,pi//2)`
`thereforetan10^(@)lttan15^(@)=2-sqrt3lt2.`
Thus option (c ) is true.
Now, `tan30^(@)=(3 tan10^(@)-tan^(3)10^(@))/(1-3tan^(2)10^(@))`
If `tan 10^(@)` is a trational number, then `(3tan10^(@)-tan^(3)10^(@))/(1-3tan^(2)10^(@))` must be a rational number, which is not true,
Hence, `tan10^(@)` is an irrational number.