Rewrite the expression as a simplified expression containing

Rewrite the expression as a simplified expression containing one term. cos (alpha + beta) cos beta + sin(alpha + beta) sin beta cos (alpha + beta)cos beta + sin (alpha + beta) sin beta = (Type an expression. Simplify your answer.)

Solution

cos( alpha + beta) cos beta + sin( alpha + beta) sin beta

this equaion is of the form

cosA cosB + sinA sinB which is equal to cos(A-B)

so we wrie the given equation as

cos ( (alpha+beta) - beta)

cos alpha

therefore

cos(alpha+beta)cos beta+sin(alpha+beta)sin beta= cos alpha