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Double-angle quotient simplified to tan x, and an equation whose common factor gives extra solutions

Double-angle quotient simplified to tan x, and an equation whose common factor gives extra solutions

IB Year 6 | Grade 12
6 marks
  1. Show that \(\frac{1-\cos2x+\sin x}{\sin2x+\cos x}=\tan x\), for values of \(x\) where the denominator is non-zero.[3]
  2. Solve the equation \(1-\cos2x+\sin x=\sin2x+\cos x\) for \(0\le x\le2\pi\).[3]

Solution:

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Answer:(b) \(x=\frac{\pi}{4},\ \frac{7\pi}{6},\ \frac{5\pi}{4},\ \frac{11\pi}{6}\)

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