Compound Angle Formulae (AQA A-Level Mathematics): Flashcards

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Compound Angle Formulae
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Compound angle formulae purpose

Express trig functions of sums/differences in terms of individual angles

sin(A+B)\sin(A + B) formula

sinAcosB+cosAsinB\sin A \cos B + \cos A \sin B

sin(AB)\sin(A - B) formula

sinAcosBcosAsinB\sin A \cos B - \cos A \sin B

cos(A+B)\cos(A + B) formula

cosAcosBsinAsinB\cos A \cos B - \sin A \sin B

cos(AB)\cos(A - B) formula

cosAcosB+sinAsinB\cos A \cos B + \sin A \sin B

tan(A+B)\tan(A + B) formula

tanA+tanB1tanAtanB\frac{\tan A + \tan B}{1 - \tan A \tan B}

tan(AB)\tan(A - B) formula

tanAtanB1+tanAtanB\frac{\tan A - \tan B}{1 + \tan A \tan B}

Ordinary algebra rules for sin(A±B)\sin(A \pm B)

Do not apply

How tan\tan compound formulae are derived

Divide sine formula by cosine formula

Value of sin(θ+π2)\sin(\theta + \frac{\pi}{2})

cosθ\cos \theta

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