CAIE P1 2012 June — Question 4

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionJune
TopicStraight Lines & Coordinate Geometry

4 The point \(A\) has coordinates \(( - 1 , - 5 )\) and the point \(B\) has coordinates \(( 7,1 )\). The perpendicular bisector of \(A B\) meets the \(x\)-axis at \(C\) and the \(y\)-axis at \(D\). Calculate the length of \(C D\).
  1. Prove the identity \(\tan x + \frac { 1 } { \tan x } \equiv \frac { 1 } { \sin x \cos x }\).
  2. Solve the equation \(\frac { 2 } { \sin x \cos x } = 1 + 3 \tan x\), for \(0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }\).