Specialist Mathematics Β· Unit 2 Β· Trigonometry and functions Β· Trigonometric identities
Prove and apply the angle sum, difference and double-angle identities for sines and cosines. sin(π΄ + π΅) = sin(π΄) cos(π΅) + cos(π΄) sin(π΅) sin(π΄ β π΅) = sin(π΄) cos(π΅) β cos(π΄) sin(π΅) cos(π΄ + π΅) = cos(π΄) cos(π΅) β sin(π΄) sin(π΅) cos(π΄ β π΅) = cos(π΄) cos(π΅) + sin(π΄) sin(π΅) sin(2π΄) = 2 sin(π΄) cos(π΄) cos(2π΄) = cos2(π΄) β sin2(π΄) = 1 β 2 sin2(π΄) = 2 cos2(π΄) β 1
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Prove and apply multi-angle trigonometric identities up to angles of 4π₯ using the identities listed above, e.g. cos(4π₯) = 8 cos4(π₯) β 8 cos2(π₯) + 1 and cosec(2π₯) β cot(2π₯) = tan(π₯). Specialist Mathematics 2025 v1.4
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Prove and apply the identities for products of sines and cosines expressed as sums and differences. sin(π΄) sin(π΅) = 1 2 (cos(π΄ β π΅) β cos(π΄ + π΅)) cos(π΄) cos(π΅) = 1 2 (cos(π΄ β π΅) + cos(π΄ + π΅)) sin(π΄) cos(π΅) = 1 2 (sin(π΄ + π΅) + sin(π΄ β π΅)) cos(π΄) sin(π΅) = 1 2 (sin(π΄ + π΅) β sin(π΄ β π΅))