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Verified answer
2 cos 15 (sin 15 + cos 15) - 1 == (2 cos 15 sin 15) + (2cos² 15 - 1)
= sin 2(15) + cos 2(15)
= sin 30 + cos 30
= 1/2 + 1/2 √3
= 1/2 (1 + √3)