Hello,

cos(45) is supposed to b a known value, that is sqrt(2)/2

this can be "proved" this way :

cos(45)=sin(45) (because cos(90-x)=sin(x))

we know that cosē(x)+sinē(x)=1

hence 2cosē(x)=1

cosē(x)=1/2

cos(x)=+ or - 1/sqrt(2)=+ or - sqrt(2)/2

since 45 is in the first quadrant, its cosine is positive. hence it's sqrt(2)/2