Additional Mathematics 0606 / Trigonometry / 1.171.17: Cotangent equation and secant identity0606/12/O/N/17 — Question 11 · 14 marksMark as done · Save for later · Show all solutions(a)Solve 2cot(ϕ+35∘)=52\cot(\phi + 35^{\circ}) = 52cot(ϕ+35∘)=5 for 0∘≤ϕ≤360∘0^{\circ} \le \phi \le 360^{\circ}0∘≤ϕ≤360∘.[4]▸ Answer(b)(i)Show that secθcotθ+tanθ=sinθ\tfrac{\sec \theta}{\cot \theta + \tan \theta} = \sin \thetacotθ+tanθsecθ=sinθ.[3]▸ Answer(b)(ii)Hence solve sec3θcot3θ+tan3θ=−32\tfrac{\sec 3\theta}{\cot 3\theta + \tan 3\theta} = -\tfrac{\sqrt{3}}{2}cot3θ+tan3θsec3θ=−23 for −π2≤θ≤π2-\tfrac{\pi}{2} \le \theta \le \tfrac{\pi}{2}−2π≤θ≤2π, giving your answers in terms of π\piπ.[4]▸ Answer▸ Official mark scheme← 1.16: Sine curve constants from amplitude and period1.30: Eliminating the parameter with sec and tan →
