IB Math HL Trigonometry Test 4 2015 P1 Q1

IB Math HL Trigonometry Test 4 2015 P1 Q1

IB Year 6 | Grade 12
9 marks
  1. Use the formula for \(\cos(A+B)\) to show that \(4\cos(x+\frac{\pi}{6})\cos(x+\frac{\pi}{3})=\sqrt3-2\sin2x\).[3]
  2. Hence find the exact value of \(4\cos\frac{5\pi}{12}\cos\frac{7\pi}{12}\).[3]
  3. Solve \(4\cos(x+\frac{\pi}{6})\cos(x+\frac{\pi}{3})=\sqrt3-\sqrt2\) for \(0\le x\le2\pi\).[3]

Solution:

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Answer:(b) \(\sqrt3-2\). (c) \(x=\frac{\pi}{8},\frac{3\pi}{8},\frac{9\pi}{8},\frac{11\pi}{8}\).

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