Additional Mathematics 0606 / Trigonometry / 3.833.83: Secant identity and equation0606/23/O/N/22 — Question 5 · 8 marksMark as done · Save for later · Show all solutions(a)Show that sin x1−cos x+cos x1−sin x=sec x\dfrac{\mathrm{sin}\,x}{1-\mathrm{cos}\,x}+\dfrac{\mathrm{cos}\,x}{1-\mathrm{sin}\,x}=\mathrm{sec}\,x1−cosxsinx+1−sinxcosx=secx.[4]▸ Answer(b)Hence solve the equation sin θ1−cos θ+cos θ1−sin θ=23\dfrac{\mathrm{sin}\,\theta}{1-\mathrm{cos}\,\theta}+\dfrac{\mathrm{cos}\,\theta}{1-\mathrm{sin}\,\theta}=\dfrac{2}{\sqrt{3}}1−cosθsinθ+1−sinθcosθ=32 for −360∘⩽θ⩽360∘-360^{\circ}\leqslant \theta\leqslant 360^{\circ}−360∘⩽θ⩽360∘.[4]▸ Answer▸ Official mark scheme← 3.82: Line intersecting cubic curve3.23: Normal to tan curve: midpoint of AB →
