Compound Angle Formulae (Leaving Cert Mathematics): Flashcards

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Compound Angle Formulae
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Compound angle formulae definition

Trig identities for sin/cos/tan of sum or difference of 2 angles

sin⁡(A+B)\sin(A + B) formula

sin⁡Acos⁡B+cos⁡Asin⁡B\sin A \cos B + \cos A \sin B

sin⁡(A−B)\sin(A - B) formula

sin⁡Acos⁡B−cos⁡Asin⁡B\sin A \cos B - \cos A \sin B

cos⁡(A+B)\cos(A + B) formula

cos⁡Acos⁡B−sin⁡Asin⁡B\cos A \cos B - \sin A \sin B

cos⁡(A−B)\cos(A - B) formula

cos⁡Acos⁡B+sin⁡Asin⁡B\cos A \cos B + \sin A \sin B

tan⁡(A+B)\tan(A + B) formula

tan⁡A+tan⁡B1−tan⁡Atan⁡B\frac{\tan A + \tan B}{1 - \tan A \tan B}

tan⁡(A−B)\tan(A - B) formula

tan⁡A−tan⁡B1+tan⁡Atan⁡B\frac{\tan A - \tan B}{1 + \tan A \tan B}

Applications of compound angle formulae

Solve trig eqs, prove identities, simplify expressions

Ordinary algebra rules for sin⁡(A+B)\sin(A + B)

Do not apply

Derivation of tangent compound formulae

Divide sine formula by cosine formula

sin⁡(75∘)\sin(75^\circ) value

6+24\frac{\sqrt{6} + \sqrt{2}}{4}

cos⁡(15∘)\cos(15^\circ) value

6+24\frac{\sqrt{6} + \sqrt{2}}{4}

sin⁡(θ+π2)\sin(\theta + \frac{\pi}{2}) equals

cos⁡θ\cos \theta

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