1.25: Tangent–sine identity and parametric elimination

0606/13/M/J/17 — Question 7 · 7 marks

(a)
Show that tan⁡2θ+sin⁡2θcos⁡θ+sec⁡θ=tan⁡θsin⁡θ\tfrac{\tan^{2}\theta + \sin^{2}\theta}{\cos \theta + \sec \theta} = \tan \theta \sin \theta.
[4]
(b)
Given that x=3sin⁡ϕx = 3\sin \phi and y=3cos⁡ϕy = \tfrac{3}{\cos \phi}, find the numerical value of 9y2−x2y29y^{2} - x^{2}y^{2}.
[3]