Cos113°30 cos 53°30' + sin 113°30' sin 53°30'

Cos113°30'cos53°30'+sin113°30'sin53°30'=1/2(cos(113°30'+53°30')+cos(113°30'-53°30'))+1/2(cos(113°30'-53°30')-cos(113°30'+53°30'))=1/2(cos167°+cos60°)+1/2(cos60°-cos167°)=1/2(cos167°+cos60°)-1/2(cos167°+cos60°)=0