Question

If `alpha,beta,gamma` are real numbers, then without expanding at any stage, show that `|1cos(beta-alpha)"cos"(gamma-alpha)"cos"(alpha-beta)1"cos"(gamma-beta)"cos"(alpha-gamma)"cos"(beta-gamma)1|=0`

Answer 1

`|{:(1,,cosalpha cos beta + sin alphasin beta,,cos alpha cos gamma+sin alpha sin gamma),(cos alpha cos beta+sin alpha sin beta,,1,,cos gamma cos beta + sin gamma sin beta),(cos alpha cos gamma + sin alpha sin gamma,,cos beta cos gamma + sin beta sin gamma,,1):}|`
`|{:(sin alpha,,sin alpha,,0),(cos beta,,sin beta,,0),(cos gamma,,sin gamma,,0):}|xx|{:( cos alpha,,sin alpha,,0),( cos beta,,sin beta,,0),(cos gamma,,sin gamma,,0):}|`
`=0xx0=0`