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Trigonometric Identities and Equations

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Question 7

The diagram shows parts of the curves y=12cos⁡2θy = 12\cos^2\thetay=12cos2θ and y=11−4tan⁡θcos⁡θy = 11 - 4\tan\theta \cos\thetay=11−4tanθcosθ, where θ \theta\,θ is in degrees.

Coordinate axes labelled y and θ show the curves y = 12cos²θ and y = 11 − 4tanθ cosθ, with two open circles on the second curve.

a.

Show that the equation 11−4tan⁡θcos⁡θ=12cos⁡2θ11 - 4\tan\theta \cos\theta = 12\cos^2\theta11−4tanθcosθ=12cos2θ can be expressed in the form 12sin⁡2x−4sin⁡x−1=012\sin^2 x - 4\sin x - 1 = 012sin2x−4sinx−1=0

[2]
b.

Solve the inequality 11−4tan⁡θcos⁡θ>12cos⁡2θ11 - 4\tan\theta \cos\theta > 12\cos^2\theta11−4tanθcosθ>12cos2θ for 0∘≤θ<360∘0^\circ \leq \theta < 360^\circ0∘≤θ<360∘

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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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