Show that sin 105∘ + cos105∘ = 1√2
We have LHS = sin 105∘ + cos105∘
= sin (60∘+45∘) + cos (60∘+45∘)
= (sin 60∘cos 45∘+cos 60∘sin 45∘) + (cos 60∘ cos 45∘ - sin 60∘sin 45∘)
={(√32×1√2)+(12×1√2)}+{(12×1√2)−(√32×1√2)}
=(√32√2+12√2+12√2−√32√2)=1√2 = RHS.