The t-formulaeEdexcel A-Level Further Maths: Mind map

Exam questions on The t-formulae

1. Given that $\theta$ is acute and $\tan\frac{\theta}{2}=\frac12$.
   Find the exact value of $\operatorname{cosec}\theta+\cot\theta$.2 marks
2. Let $t=\tan\frac{x}{2}$, where $0<x<\pi$ and $x\neq\frac{\pi}{2}$.
   Show that $\sec x+\tan x=\dfrac{1+t}{1-t}$.2 marks
3. Consider the equation $3\cos x+4\sin x=2$ for $0\le x<2\pi$, and let $t=\tan\frac{x}{2}$.
   Show that the equation can be written as $5t^2-8t-1=0$.3 marks