How do I prove that sinxsinysinz+cosxcosycosz<=1 , x,y,z in R?

Answer 1

sin x ≤ 1

cos x ≤ 1

(sin x)(sin y)(sin z) + (cos x)(cos y)(cos z) ≤ (sin x)(sin y) + (cos x)(cos y)

(sin x)(sin y) + (cos x)(cos y) = cos (x - y)

cos (x - y) ≤ 1

(sin x)(sin y)(sin z) + (cos x)(cos y)(cos z) ≤ 1

QED