Since cos 45° = 1/√2 = sin 45°

cos 30° = √3/2

sin 30° = 1/2

∴ cos 45° cos 30° + sin 45° sin 30° = (1/√2)×(√3/2) + (1/√2)(1/2)

= (√3 / 2√2) + (1 / 2√2)

= (√3 + 1) / (2√2)