Trigonometric proofs and applicationsAQA A-Level Maths: Flashcards

What these 13 flashcards ask

State \sin(A+B).
State \cos(A+B).
State \sin2A.
State three forms of \cos2A.
State \tan2A.
Pythagorean identities involving \tan and \cot?
Which side should you start a proof from?
Why should you not cross-multiply when proving an identity?
How do you disprove a general statement?
Greatest and least values of \cos\theta+\sin\theta?
Range of a projectile launched at speed u and angle \theta?
Why do two launch angles give the same range?
Components of a force F at angle \alpha to the x-axis?

Exam questions on Trigonometric proofs and applications

A student sets out to prove the identity $\frac{\sin2\theta}{1+\cos2\theta}\equiv\tan\theta$ .
State the values of $\theta$ in the interval $0\le\theta\le2\pi$ for which the identity is not valid because both sides are undefined.2 marks
Let $f(x)=\sin^4x-\cos^4x$ , where $x$ is in radians.
Hence solve $f(x)=\frac12$ for $0\le x\le\pi$ .2 marks
It is claimed that $\cos\theta+\sin\theta\equiv\sqrt2\cos\left(\theta-\frac{\pi}{4}\right)$ for all values of $\theta$ .
Prove that the claim is true.3 marks

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).