Double-angle identity for cosine used to solve a quadratic equation in cos x over a full turn
Double-angle identity for cosine used to solve a quadratic equation in cos x over a full turn
5 marks
- Show that \(4\cos2x+10\cos x\) can be written as \(8\cos^2x+10\cos x-4\).[2]
- Hence, or otherwise, find all values of \(x\), where \(0^\circ\leq x\leq360^\circ\), that satisfy \(4\cos2x+10\cos x+1=0\).[3]
Solution:
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Answer:(b) \(x=75.5^\circ,\ 284.5^\circ\)
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