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1.7.21 Use identities to solve equations (A-level only)

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Question 9
a.

Show that the equation

4cos⁡α+1=3sin⁡αtan⁡α 4\cos \alpha + 1 = 3 \sin \alpha \tan \alpha 4cosα+1=3sinαtanα

can be written in the form

7cos⁡2α+cos⁡α−3=0 7\cos^2 \alpha + \cos \alpha - 3 = 0 7cos2α+cosα−3=0
[3]
b.

A light-sensitive robotic arm measures the angle ϕ\phiϕ (in radians) of incoming radiation. The arm reaches a steady state when ϕ\phiϕ satisfies:

4cos⁡3ϕ+1=3sin⁡3ϕtan⁡3ϕ 4\cos 3\phi + 1 = 3 \sin 3\phi \tan 3\phi 4cos3ϕ+1=3sin3ϕtan3ϕ

Determine all possible values for ϕ\phiϕ in the interval 0≤ϕ<2π30 \le \phi < \frac{2\pi}{3}0≤ϕ<32π​, giving your answers to 2 decimal places.

[6]

1.7.21 Use identities to solve equations (A-level only) Questions

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