Question 0808a

In a triangle ${ABC,}$ ${AB = 1,}$ ${BC = 4}$ and angle ${ABC = \theta}$ radians. Given that ${\theta}$ is a sufficiently small angle, show that for constants ${a}$ and ${b}$ to be determined.

Given that ${f(x) = \tan(2 x + \frac{3}{4}\pi),}$ find ${f(0),}$ ${f'(0)}$ and ${f''(0).}$ Hence find the first 3 terms in the Maclaurin series of ${f(x).}$