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Trigonometric Identities and Equations

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Question 60

The diagram shows parts of the curves y=4cos⁡2θy = 4\cos^2\thetay=4cos2θ and y=3y = 3y=3, where θ \theta\,θ is in degrees.

A coordinate-style diagram showing the curves y = 4 cos²θ and y = 3 over a horizontal θ-axis from 0 to 360 degrees and a vertical y-axis from 0 to 4.

a.

Show that the equation 3=4cos⁡2θ3 = 4\cos^2\theta3=4cos2θ can be expressed in the form 4sin⁡2x−1=04\sin^2 x - 1 = 04sin2x−1=0

[2]
b.

Solve the inequality 3>4cos⁡2θ 3 > 4\cos^2\theta\,3>4cos2θ 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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