Question 7 - A-Level Maths

1. Express $\frac { \tan ^ { 2 } \theta - 1 } { \tan ^ { 2 } \theta + 1 }$ in the form $a \sin ^ { 2 } \theta + b$, where $a$ and $b$ are constants to be found. [3]
2. Hence, or otherwise, and showing all necessary working, solve the equation $$\frac { \tan ^ { 2 } \theta - 1 } { \tan ^ { 2 } \theta + 1 } = \frac { 1 } { 4 }$$ for $- 90 ^ { \circ } \leqslant \theta \leqslant 0 ^ { \circ }$.
\includegraphics[max width=\textwidth, alt={}, center]{ea402a1d-3632-4637-9198-2365715b5246-11_549_796_267_717} The diagram shows the graphs of $y = \sin x$ and $y = 2 \cos x$ for $- \pi \leqslant x \leqslant \pi$. The graphs intersect at the points $A$ and $B$.
1. Find the $x$-coordinate of $A$.
2. Find the $y$-coordinate of $B$.