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Identity for the sum of sixth powers of sine and cosine, used for an exact value at pi over 12

Identity for the sum of sixth powers of sine and cosine, used for an exact value at pi over 12

IB Year 6 | Grade 12
6 marks
  1. Show that \(\sin^6x+\cos^6x=1-\dfrac34\sin^22x\).[3]
  2. Hence find the exact value of \(\sin^6\dfrac{\pi}{12}+\cos^6\dfrac{\pi}{12}\).[3]

Solution:

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Answer:(b) \(\dfrac{13}{16}\)

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