Show that sin (α-30°)+cos (α+30°) = (√3 - √1)/√2 × sin (α+45°)

Answer 1

just crank it out...
sin(α-30°)+cos(α+30°)
= sinα cos30 - cosα sin30 + cosα cos30 - sinα sin30
= √3/2 sinα - 1/2 cosα + √3/2 cosα - 1/2 sinα
= (√3/2 - 1/2)sinα + (√3/2 - 1/2) cosα
= (√3-1)/2 (sinα+cosα)
= (√3/-1)/√2 (sinα/√2 + cosα/√2)
= (√3-1)/√2 sin(α+45)