3. trignometrical ratios,functions and identities — ગણિત ધોરણ 11 સાયન્સ — Question

$\cos {15^o} = \cos ({45^o} - {30^o}) = \frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}=$ irrational

$\therefore \,\,\,\sin {15^o}\cos {15^o} = \frac{1}{2}(2\sin {15^o}\cos {15^o})$

$ = \frac{1}{2}\sin {30^o} = \frac{1}{2}.\frac{1}{2} = \frac{1}{4} =$ rational  

$\therefore \, \sin {15^o}\cos {75^o} = \sin {15^o}\sin {15^o} = {\sin ^2}{15^o}$

$ = {\left( {\frac{{\sqrt 3 - 1}}{{2\sqrt 2 }}} \right)^2} = \frac{{4 - 2\sqrt 3 }}{8}=$ irrational