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( +)cos + sin( + )sin

= (coscos - sinsin )cos + (sincos + cossin)sin

= coscos^2 - sincos^2 + sincos sin + cossin^2

= coscos^2 + cossin^2 + sincos sin - sincos^2

= cos( cos^2 + sin^) + sincos(sin - cos)

= cos + sincos(sin - cos)