Trigonometry help (1 Viewer)

[Leffife]

Simplify:
sin A cos (A - B) + cos A sin (A - B)

 

[Carrotsticks]

Recognise the Compound Angle formula with X = A and Y = A-B

sinXcosY + cosXsinY = sin(X+Y) = sin(A+A-B) = sin(2A-B).

 

[RivalryofTroll]

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)

 

[Leffife]

Yup thank you.