Question
Question: Which of the following number is rational...
Which of the following number is rational
A
sin15o
B
cos15o
C
sin15o.cos15o
D
sin15o.cos75o
Answer
sin15o.cos15o
Explanation
Solution
sin15o = sin(45o−30o) = 223−1 = irrational
⇒ cos15o=cos(45o−30o)=223+1 = irrational
sin15o.cos15o=21(2sin15ocos15o)=21sin30o=41= rational
sin15o.cos75o=sin15o.sin15o=sin215o
= (223−1)2=84−23= irrational.