The value of [cosx, sinx]• [cos(a + x), sin( a + x)] does depend on the value of a, but does

Question

not depend on the value of x. Explain why.

Answer 1

just do the dot product. You get

cosx*cos(a+x) + sinx*sin(a+x)
= cosx*cosa*cosx - cosx*sina*sinx + sinx*sina*cosx + sinx*cosa*sinx
= cosa(cos^2x+sin^2x)
= cosa