Additional Mathematics 0606 / Trigonometry / 1.291.29: Cosecant identity and tangent equation0606/13/O/N/16 — Question 8 · 9 marksMark as done · Save for later · Show all solutions(a)(i)Show that cscθcscθ−sinθ=sec2θ\tfrac{\csc \theta}{\csc \theta - \sin \theta} = \sec^{2}\thetacscθ−sinθcscθ=sec2θ.[3]▸ Answer(a)(ii)Hence solve cscθcscθ−sinθ=4\tfrac{\csc \theta}{\csc \theta - \sin \theta} = 4cscθ−sinθcscθ=4 for 0∘<θ<360∘0^{\circ} < \theta < 360^{\circ}0∘<θ<360∘.[3]▸ Answer(b)Solve 3tan(x+π4)=1\sqrt{3}\tan\left(x + \tfrac{\pi}{4}\right) = 13tan(x+4π)=1 for 0<x<2π0 < x < 2\pi0<x<2π, giving your answers in terms of π\piπ.[3]▸ Answer▸ Official mark scheme← 1.28: Sketch of a modulus cosine graph2.6: Prove tan–cot identity and solve linear equation →
