Trigonometric Proof (AQA A-Level Mathematics): Flashcards

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Trigonometric Proof
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Pythagorean identity: sin⁡2θ+cos⁡2θ\sin^2 \theta + \cos^2 \theta

sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1

Pythagorean identity: 1+tan⁡2θ1 + \tan^2 \theta

1+tan⁡2θ=sec⁡2θ1 + \tan^2 \theta = \sec^2 \theta

Pythagorean identity: csc⁡2θ\csc^2 \theta

csc⁡2θ=1+cot⁡2θ\csc^2 \theta = 1 + \cot^2 \theta

Reciprocal identity: csc⁡θ\csc \theta

csc⁡θ=1sin⁡θ\csc \theta = \frac{1}{\sin \theta}

Reciprocal identity: sec⁡θ\sec \theta

sec⁡θ=1cos⁡θ\sec \theta = \frac{1}{\cos \theta}

Quotient identity: tan⁡θ\tan \theta

tan⁡θ=sin⁡θcos⁡θ\tan \theta = \frac{\sin \theta}{\cos \theta}

Double angle identity: sin⁡2θ\sin 2\theta

sin⁡2θ=2sin⁡θcos⁡θ\sin 2\theta = 2\sin \theta \cos \theta

Which side to start with in trig proofs

The more complex side

Technique to recognise patterns in proofs

Convert everything to sine and cosine

Statement concluding a proven identity

LHS = RHS

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