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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 153

It is given that θ \theta\,θ satisfies the equation

sin⁡(2θ−45°)=3cos⁡(2θ−45°)\sin(2\theta - 45°) = 3\cos(2\theta - 45°)sin(2θ−45°)=3cos(2θ−45°)

a.

Show that tan⁡2θ=−2\tan 2\theta = -2tan2θ=−2.

[3]
b.

Hence find, in surd form, the exact value of tan⁡θ\tan\thetatanθ, given that θ \theta\,θ is an obtuse angle.

[5]
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3 Unit A2 1: Pure Mathematics (A-level only) Questions

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