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Trigonometric Identities and Equations

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Question 25

The diagram shows parts of the curves y=6cos⁡2θy = 6\cos^2\thetay=6cos2θ and y=5−tan⁡θcos⁡θy = 5 - \tan\theta \cos\thetay=5−tanθcosθ, where θ \theta\,θ is in degrees.

Diagram showing parts of the curves y = 6cos²θ and y = 5 − tanθ cosθ, where θ is in degrees.

a.

Show that the equation 5−tan⁡θcos⁡θ=6cos⁡2θ5 - \tan\theta \cos\theta = 6\cos^2\theta5−tanθcosθ=6cos2θ can be expressed in the form 6sin⁡2θ−sin⁡θ−1=06\sin^2\theta - \sin\theta - 1 = 06sin2θ−sinθ−1=0

[2]
b.

Solve the inequality 5−tan⁡θcos⁡θ>6cos⁡2θ5 - \tan\theta \cos\theta > 6\cos^2\theta5−tanθcosθ>6cos2θ for 0∘≤θ<360∘0^\circ \leq \theta < 360^\circ0∘≤θ<360∘

[5]
Markscheme

Trigonometric Identities and Equations Questions

  1. A Level
  2. /Maths
  3. /Trigonometric Identities and Equations

322 exam-style questions on Edexcel A Level Maths Trigonometric Identities and Equations, covering 10.1 Angles in all four Quadrants, 10.2 Exact Values of Trigonometric Ratios, 10.3 Trigonometric Identities, 10.4 Solving Trigonometric Equations, 10.5 Harder Trigonometric Equations, and 10.6 Equations and Identities. Each one has a worked solution and a mark scheme showing where the marks go.

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