Harmonic form and trigonometric proofEdexcel A-Level Maths: Mind map

Exam questions on Harmonic form and trigonometric proof

1. Let $h(\theta)=7\cos\theta-24\sin\theta$, where $\theta$ is measured in degrees.
   Find the maximum value of $h(\theta)$ and the smallest positive value of $\theta$ at which it occurs, giving $\theta$ to 1 decimal place.2 marks
2. Consider the expression $E=\cos x\cos2x+\sin x\sin2x$.
   Prove that $E\equiv\cos x$, and hence solve $E=\frac12$ for $0\le x<360^\circ$.2 marks
3. Consider the identity $\dfrac{\sin2\theta}{1+\cos2\theta}\equiv\tan\theta$.
   Prove that the identity is true.3 marks