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Trigonometry help (1 Viewer)
- Thread starter Leffife
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Carrotsticks
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Recognise the Compound Angle formula with X = A and Y = A-B
sinXcosY + cosXsinY = sin(X+Y) = sin(A+A-B) = sin(2A-B).
sinXcosY + cosXsinY = sin(X+Y) = sin(A+A-B) = sin(2A-B).
RivalryofTroll
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sinA(cosAcosB+sinAsinB) + cosA(sinAcosB - sinBcosA)
= sinAcosAcosB + sin^2AsinB + sinAcosAcosB - sinBcos^2A
= 2sinAcosAcosB + sin^2AsinB - cos^2AsinB
= sin2AcosB - sinB(cos^2A - sin^2A)
= sin2AcosB - cos2AsinB
= sin(2A - B)
= sinAcosAcosB + sin^2AsinB + sinAcosAcosB - sinBcos^2A
= 2sinAcosAcosB + sin^2AsinB - cos^2AsinB
= sin2AcosB - sinB(cos^2A - sin^2A)
= sin2AcosB - cos2AsinB
= sin(2A - B)
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