[tex]\displaystyle\\
\sin15^o \times \cos75+\cos^2 165^o =\\\\
=\sin15^o \times \sin(90-75)+(1-\sin^2 165^o) =\\\\
=\sin15^o \times \sin15+1-\sin^2 (180^o-165^o) =\\\\
=\underline{\sin^2 15^o}+1-\underline{\sin^2 15^o} = \boxed{\bf \texttt{\bf 1}}[/tex]
