Additional Mathematics 0606 / Trigonometry / 2.182.18: Tan–cot identity and linear combination0606/22/O/N/16 — Question 6 · 8 marksMark as done · Save for later · Show all solutions(i)Prove that cosx1+tanx−sinx1+cotx=cosx−sinx\dfrac{\cos x}{1 + \tan x} - \dfrac{\sin x}{1 + \cot x} = \cos x - \sin x1+tanxcosx−1+cotxsinx=cosx−sinx.[4]▸ Answer(ii)Hence solve the equation cosx1+tanx−sinx1+cotx=3sinx−4cosx\dfrac{\cos x}{1 + \tan x} - \dfrac{\sin x}{1 + \cot x} = 3\sin x - 4\cos x1+tanxcosx−1+cotxsinx=3sinx−4cosx for −180°<x<180°-180^{\degree} < x < 180^{\degree}−180°<x<180°.[4]▸ Answer▸ Official mark scheme← 2.6: Prove tan–cot identity and solve linear equation2.28: Cosine rule with surds and area →
