Which of the following number(s) is/are rational? `sin15^0` (b) `cos15^0` `sin15^0cos15^0` (d) `sin15^0cos75^0`

Options

A. `sin15^(@)`
B. `cos15^(@)`
C. `sin15^(@)cos15^(@)`
D. `sin15^(@)cos75^(@)`

Answer

C

Explanation

We have,
`sin 15^(@)=sin(45^(@)-30^(@))=(sqrt3-1)/(2sqrt2)`
`impliessin15^(@)=1/4(sqrt6-sqrt2),` whichis an irrational number
`sin 15^(@)cos 15^(@)=1/2sin 30^(@)=1/4,` which a rational number
`sin 15^(@)cos 75^(@)=sin^(2)15^(@)=1/2(1-cos30^(@))=(2-sqrt3)/(4)`
which is an irrational number.