Additional Mathematics 0606 / Trigonometry / 1.61.6: Secant identity and cosecant equation0606/11/M/J/20 — Question 10 · 12 marksMark as done · Save for later · Show all solutions(a)(i)Show that 1secθ−1−1secθ+1=2cot2θ\tfrac{1}{\sec\theta - 1} - \tfrac{1}{\sec\theta + 1} = 2\cot^{2}\thetasecθ−11−secθ+11=2cot2θ.[3]▸ Answer(a)(ii)Hence solve 1sec2x−1−1sec2x+1=6\tfrac{1}{\sec 2x - 1} - \tfrac{1}{\sec 2x + 1} = 6sec2x−11−sec2x+11=6 for −90°<x<90°-90^{\degree} < x < 90^{\degree}−90°<x<90°.[5]▸ Answer(b)Solve csc(y+π3)=2\csc\left(y + \tfrac{\pi}{3}\right) = 2csc(y+3π)=2 for 0≤y≤2π0 \le y \le 2\pi0≤y≤2π radians, giving your answers in terms of π\piπ.[4]▸ Answer▸ Official mark scheme← 1.5: Period and sketch of a cosine graph1.15: Tangent equation and graph sketch →
