Prove that cosθ+sinθtanθ≡secθ\cos \theta + \sin \theta \tan \theta \equiv \sec \thetacosθ+sinθtanθ≡secθ
Hence verify that 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, are π3,2π3,4π3,5π3\displaystyle \frac{\pi}{3}, \frac{2\pi}{3}, \frac{4\pi}{3}, \frac{5\pi}{3}3π,32π,34π,35π
274 exam-style questions on Edexcel A Level Maths Trigonometric Functions, covering 6.1 Secant, Cosecant and Cotangent, 6.2 Graphs of Sec x, Cosec x and Cot x, 6.3 Using Sec x, Cosec x and Cot x, 6.4 Trigonometric Identities, and 6.5 Inverse Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.