Evaluate |(cosαcosβ, cosαsinβ, - sinα), (sinαcosβ, sinαsinβ, cosα)|

Question

Evaluate

\(\begin{vmatrix} cos\alpha cos\beta&cos\alpha sin\beta & -sin\alpha \\[0.3em] sin\alpha cos\beta& sin\alpha sin\beta &cos\alpha \\[0.3em] \end{vmatrix}\)

Answer 1

expand along c₃ 

-sin α (-sin α sin²β – sin α cos²β) + cosa (cosα cos² β+cosα sin²β) 

= sin²α (sin²β + cos²β)+cos²α (cos²β + sin²β) 

= sin²α + cos²α= 1