2007 SQA Advanced Higher Maths no.13 Parametric equations

Finding the equation of a tangent to a curve defined by parametric equations. Finding the second derivative and using this to simplify a second order differential expression. Lengthier than normal due to a geometric explanation of the question in part a, and dealing with trig identities involving the reciprocal functions in part b. Instructional exercise consisting of question 13 from the 2007 SQA Advanced Higher Mathematics exam. Set out in stages of 'try then check' the worked solution to each part of the question.