Trigonometric Proof (Edexcel A-Level Mathematics): Quizzes

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Trigonometric Proof
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For which values must a trigonometric identity be true when proving it?

All values within the domain

Which side should you start with when proving a trigonometric identity?

The more complex side

Which Pythagorean identity involves tanθ\tan \theta and secθ\sec \theta?

1+tan2θ=sec2θ1 + \tan^2 \theta = \sec^2 \theta

What is the reciprocal identity for secθ\sec \theta?

secθ=1cosθ\sec \theta = \frac{1}{\cos \theta}

What is the quotient identity for tanθ\tan \theta?

tanθ=sinθcosθ\tan \theta = \frac{\sin \theta}{\cos \theta}

What is the double angle identity for sin2θ\sin 2\theta?

sin2θ=2sinθcosθ\sin 2\theta = 2\sin \theta \cos \theta

Which Pythagorean identity involves cscθ\csc \theta and cotθ\cot \theta?

csc2θ=1+cot2θ\csc^2 \theta = 1 + \cot^2 \theta

What technique helps recognize patterns more easily in complex identities?

Converting to sine and cosine

What statement indicates that a trigonometric identity has been proven?

LHS = RHS

In proving sec2θtan2θ=1\sec^2 \theta - \tan^2 \theta = 1, which substitution is used?

sec2θ=1+tan2θ\sec^2 \theta = 1 + \tan^2 \theta

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