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Sum of the sixth powers of sine and cosine in terms of a double angle, then an equation

Sum of the sixth powers of sine and cosine in terms of a double angle, then an equation

IB Year 6 | Grade 12
7 marks
  1. Show that \(\sin^6x+\cos^6x=1-\frac34\sin^22x\).[2]
  2. Hence solve the equation \(\sin^6x+\cos^6x=\frac{13}{16}\) for \(0\le x\le\pi\).[5]

Solution:

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Answer:(b) \(x=\frac{\pi}{12},\ \frac{5\pi}{12},\ \frac{7\pi}{12},\ \frac{11\pi}{12}\)

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