The given question seem incomplete
Rewrite the expression as a simplified expression containing one term
cos (α + β)cos(β) + sin( α + β)sin(β)
Answer:
The simplified form of the given expression is cos(α)
Step-by-step explanation:
We are given the expression
cos (alpha + beta)cos(beta) + sin( alpha + beta)sin(beta)
we will proceed by expanding the given expression as
(cos(alpha)cos(beta) - sin(alpha)sin(beta))cos(beta) + (sin(alpha)cos(beta)+cos(alpha)sin(beta))sin(beta)
cos(alpha)cos^2(beta) -sin(alpha)sin(beta)cos(beta) + sin(alpha)cos(beta)sin(beta) + cos(alpha)sin^2(beta)
The two middle terms will cancel each other so we are left with
cos(alpha)cos^2(beta) + cos(alpha)sin^2(beta)
cos(alpha)[cos^2(beta) + sin^2(beta)]
cos(alpha) (1) = cos(alpha) [cos^2(beta) + sin^2(beta) = 1]
Therefore the simplified form of the given expression is cos(α)
