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Trigonometric identitiesEdexcel International A Level Maths: Mind map

The identities
Rearranging
Finding ratios

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

and $\tan\theta=\frac{\sin\theta}{\cos\theta}$

≡\equivsin⁡2+cos⁡2=1\sin^2+\cos^2=1tan⁡=sin⁡cos⁡\tan=\frac{\sin}{\cos}
Simplifying
Proofs
Exam tips

Exam questions on Trigonometric identities

  1. θ\theta is an obtuse angle with sin⁡θ=817\sin\theta=\frac{8}{17}.
    Find the exact value of sin⁡θcos⁡θ\sin\theta\cos\theta.2 marks
  2. cos⁡x=−23\cos x=-\frac23 and 180∘<x<270∘180^\circ<x<270^\circ.
    Find the exact value of tan⁡2x−sin⁡2x\tan^2x-\sin^2x.2 marks
  3. In this question, θ\theta is any angle for which the expressions are defined.
    Show that (sin⁡θ+cos⁡θ)2≡1+2sin⁡θcos⁡θ(\sin\theta+\cos\theta)^2\equiv1+2\sin\theta\cos\theta.3 marks
See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).