Trigonometry - Further Identities (AQA A-Level Mathematics): Flashcards

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Trigonometry - Further Identities
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Formula for sin(A±B)\sin(A \pm B)

sinAcosB±cosAsinB\sin A \cos B \pm \cos A \sin B

Formula for cos(A±B)\cos(A \pm B)

cosAcosBsinAsinB\cos A \cos B \mp \sin A \sin B

Formula for tan(A±B)\tan(A \pm B)

tanA±tanB1tanAtanB\frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}

Formula for sin2θ\sin 2\theta

2sinθcosθ2\sin \theta \cos \theta

Formula for cos2θ\cos 2\theta

cos2θsin2θ\cos^2 \theta - \sin^2 \theta

Formula for tan2θ\tan 2\theta

2tanθ1tan2θ\frac{2\tan \theta}{1 - \tan^2 \theta}

What determines sign in half-angle identities?

The quadrant in which the half angle lies

Product-to-sum identities convert what?

Products of sine and cosine into sums

Sum-to-product identities convert what?

Sums/differences of sines and cosines into products

Which trig functions are odd?

Sine, cosecant, tangent, cotangent

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