How do you find the distance between two askew lines in 3d space?

What basic trigonometric identity would you use to verify that sin x cos x tan x =1-cos^(2)x?

Ametalworker has a metal alloy that is 30? % copper and another alloy that is 55? % copper. how many kilograms of each alloy should the metalworker combine to create 90 kg of a 50? % copper? alloy?

Aclassmate thinks that solving a system by graphing gives an exact answer when the lines appear to cross at a grid point, but only an approximate answer when they don't. explain why this isn't true.