Prove that cosθ+sinθtanθ≡secθ\cos\theta + \sin\theta\tan\theta \equiv \sec\thetacosθ+sinθtanθ≡secθ.
Hence find the exact roots of the equation
cosθ+sinθtanθ=4cosθ\cos\theta + \sin\theta\tan\theta = 4\cos\thetacosθ+sinθtanθ=4cosθ
for 0≤θ≤2π0 \leq \theta \leq 2\pi0≤θ≤2π.
221 exam-style questions on CCEA A Level Maths 3.4 Trigonometry (A-level only), covering 3.4.1 Trigonometry (A-level only), 3.4.2 Trigonometry (A-level only), 3.4.3 Trigonometry (A-level only), 3.4.4 Trigonometry (A-level only), 3.4.5 Trigonometry (A-level only), 3.4.6 Trigonometry (A-level only), 3.4.7 Trigonometry (A-level only), and 3.4.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.