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Trigonometric Identities and Equations

Trigonometric Identities and Equations

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Question 21

Jacob has to solve the equation

3−sin⁡x=1+2cos⁡2x 3 - \sin x = 1 + 2\cos^2 x 3−sinx=1+2cos2x

where −180∘≤x<180∘-180^{\circ} \le x < 180^{\circ}−180∘≤x<180∘

Jacob’s working is as follows:

3−sin⁡x=1+2cos⁡2x2−sin⁡x=2cos⁡2x2−sin⁡x=2(1−sin⁡2x)2−sin⁡x=2−2sin⁡2x−sin⁡x=−2sin⁡2x1=2sin⁡xsin⁡x=0.5x=30∘ \begin{aligned} 3 - \sin x &= 1 + 2\cos^2 x \\ 2 - \sin x &= 2\cos^2 x \\ 2 - \sin x &= 2(1 - \sin^2 x) \\ 2 - \sin x &= 2 - 2\sin^2 x \\ -\sin x &= -2\sin^2 x \\ 1 &= 2\sin x \\ \sin x &= 0.5 \\ x &= 30^{\circ} \end{aligned} 3−sinx2−sinx2−sinx2−sinx−sinx1sinxx​=1+2cos2x=2cos2x=2(1−sin2x)=2−2sin2x=−2sin2x=2sinx=0.5=30∘​
a.

Explain the two errors that Jacob has made.

[2]
b.

Write down all the values of x x\,x that satisfy the equation

3−sin⁡x=1+2cos⁡2x 3 - \sin x = 1 + 2\cos^2 x 3−sinx=1+2cos2x

where −180∘≤x<180∘-180^{\circ} \le x < 180^{\circ}−180∘≤x<180∘

[2]
Markscheme

Trigonometric Identities and Equations Questions

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

41 exam-style questions on Edexcel AS 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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