1.

Which one of the following number (s) is/are rational?A. `sin15^(@)`B. `cos15^(@)`C. `sin15^(@)cos15^(@)`D. `sin15^(@)cos75^(@)`

Answer» Correct Answer - C
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.


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