Question 297915
{{{cos(v-u) = cos(v)*cos(u) + sin(x)*sin(y) }}}
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{{{sin(u) = 12/13}}} 
{{{sin^2(u)+cos^2(u)=1}}}
{{{(12/13)^2+cos^2(u)=1}}}
{{{144/169+cos^2(u)=169/169}}}
{{{cos^2(u)=(169-144)/169}}}
{{{cos^2(u)=25/169}}}
{{{cos(u)=0 +- 5/13}}}
Quadrant II
{{{cos(u) = -5/13}}}
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{{{cos(v)=-4/5}}} 
{{{sin^2(v) +cos^2(v)=1}}}
{{{sin^2(v)+(-4/5)^2=1}}}
{{{sin^2(v)+(16/25)=25/25}}}
{{{sin^2(v)=(25-16)/25}}}
{{{sin^2(v)=9/25}}}
{{{sin(v)=0 +- 3/5}}}
Quadrant II
{{{sin(v)=3/5}}}
Now substitute directly,
{{{cos(v-u) = cos(v)*cos(u) + sin(v)*sin(u) }}}
{{{cos(v-u) = -(4/5)*(-(5/13)) + (3/5)*(12/13) }}}
{{{cos(v-u) = 20/65+ 36/65 }}}
{{{cos(v-u) = 56/65 }}}