Equation in tangent and sine solved by factorising, and a quadratic in cos 2x from a double angle

Equation in tangent and sine solved by factorising, and a quadratic in cos 2x from a double angle

IB Year 6 | Grade 12
8 marks
  1. Solve the equation \(\tan x+2\sin x=0\) for \(-\pi\le x\le\pi\).[4]
  2. Solve the equation \(\cos4x+3\cos2x+2=0\) for \(0\le x\le\pi\).[4]

Solution:

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Answer:(a) \(x=-\pi,\ -\frac{2\pi}{3},\ 0,\ \frac{2\pi}{3},\ \pi\) (b) \(x=\frac{\pi}{3},\ \frac{\pi}{2},\ \frac{2\pi}{3}\)

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