Additional Mathematics 0606 / Trigonometry / 3.543.54: Definite integral and reciprocal trig identity0606/12/M/J/25 — Question 4 · 5 marksMark as done · Save for later · Show all solutions(a)Find ∫0πsin θ dθ\displaystyle\int_{0}^{\pi} \mathrm{sin}\,\theta\,\mathrm{d}\theta∫0πsinθdθ.[2]▸ Answer(b)Given that 0<α<π20 < \alpha < \dfrac{\pi}{2}0<α<2π, show that sec αcot α+tan α\dfrac{\mathrm{sec}\,\alpha}{\mathrm{cot}\,\alpha + \mathrm{tan}\,\alpha}cotα+tanαsecα can be written as sin α\mathrm{sin}\,\alphasinα.[3]▸ Answer▸ Official mark scheme← 3.53: Modulus equation and sine graph sketch3.55: Perpendicular bisector and triangle area →
