Trigonometric proofs and applicationsAQA A-Level Maths: Mind map

Exam questions on Trigonometric proofs and applications

1. 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
2. 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
3. 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