simplify and show all work

Question

simplify (√2/2)•(cosx+sinx) square root is only in numerator* show all work

Answer 1

cos(45°) = sqrt(2)/2 and sin(45°) = sqrt(2)/2

Thus sqrt(2)/2 * (cos x + sin x) =

sqrt(2)/2 * cos x + sqrt(2)/2 sin x =

sin(45°) cos x + cos(45°) sin x =

sin(45° + x) or sin(π/4 + x)