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sin^2α+cosαcos(π/3+a)-sin^2(π/6-α)
＝(sinα)^2＋cosα[1/2×cosα－√3/2×sinα]＋[1/2×cosα－√3/2×sinα]^2
＝(sinα)^2＋1/4×(cosα)^2－3/4×(sinα)^2
＝1/4×(sinα)^2＋1/4×(cosα)^2
＝1/4