• # question_answer If $x=\sin {{130}^{o}}\,\cos {{80}^{o}},\,\,y=\sin \,{{80}^{o}}\,\cos \,{{130}^{o}},\,\,z=1+xy,$which one of the following is true [AMU 1999] A) $x>0,\,\,y>0,\,\,z>0$ B) $x>0,\,\,y<0,\,\,0<z<1$ C) $x>0,\,\,y<0,\,\,z>1$ D) $x<0,\,\,y<0,\,0<z<1$

$x=\sin {{130}^{o}}\cos {{80}^{o}},$ $y=\sin {{80}^{o}}\cos {{130}^{o}}$ Þ $x=\cos {{40}^{o}}\cos {{80}^{o}},\,\,\,y=-\sin {{80}^{o}}\sin {{40}^{o}}$ So, $x>0$ and $y<0and$$xy<0$ Now$z=1+xy$ Þ $0<z<1$.