∵已知α+β=90°
∴β=90°-α ==>cosβ=cos(90°-α)=sinα
∵sinα+cosβ=√2
==>sinα+sinα=√2
==>sinα=√2/2
∴α=β=45°
故 sin²α+3cos²β=(√2/2)²+3(√2/2)²
=4(√2/2)²
=2.