The t-formulae (Edexcel A Level Further Maths: Further Pure 1): Exam Questions

In this question you must show all stages of your working.

Solutions relying on calculator technology are not acceptable.

Use the substitution $t=\text{tan}\frac{\theta }{2}$ to show that

$\int \frac{1}{2+\text{sin}\theta }\text{d}\theta =\int \frac{a}{t^2+bt+c}\text{d}t$

where $a$, $b$ and $c$ are constants to be determined.