If `tanalpha=sqrta` where a is not a perfect square then which of the following is a rational number

Options

A. `sin 2 alpha`
B. `tan 2 alpha`
C. `cos 2 alpha`
D. none of these

Answer

C

Explanation

We have,
`sin2 alpha=(2tanalpha)/(1+tan^(2)alpha)=(2sqrta)/(1+a),` which is an irrational number
`tan2alpha=(2 tanalpha)/(1-tan^(2)alpha)=(2sqrta)/(1-a),` which is an irrational number
`cos 2 alpha=(1-tan^(2)alpha)/(a+tan^(2)alpha)=(1-a)/(1+a),` whihc is a rational number.