Which of the following numbers is rational?

Options

A. sin `15^(@)`
B. `cos 15^(@)`
C. sin `15^(@)` cos `15^(@)`
D. sin `15^(@)` cos `75^(@)`

Answer

C

Explanation

Since, `sin 15^(@) = (1)/(2) sqrt(2-sqrt(3)) and cos 15^(@) = (1)/(2) sqrt(2+sqrt(3))`
and `sin 15^(@) cos 75^(@) = sin 15^(@).sin 15^(@) = (1)/(4)(2 - sqrt(3))`
Therefore, all these values are irrational and
`sin 15^(@) cos 15^(@) = (1)/(2).2 sin 15^(@) cos 15^(@)`
`=(1)/(2).sin 30^(@) = (1)/(4)`, which is rational.