Rewrite the expression as a simplified expression containing one term cos alpha - beta

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)

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)

rounding to the nearest thousandth would be 452,000

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step-by-step explanation:

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