Consider the following:<br>I. 1-\sin^{6}\alpha=\cos^{2}\alpha(\cos^{4}\alpha-3\cos^{2}\alpha+3)<br>II. \cos^{8}\alpha-\sin^{8}\alpha=2\sin^{2}\alpha(1-\cos^{4}\alpha+\sin^{2}\alpha\cos^{2}\alpha)<br>Which of the above is/are identities?
- A. I only ✓
- B. II only
- C. Both I and II
- D. Neither I nor II
Correct Answer: A. I only
Explanation
Expanding statement I using 1-\sin^6\alpha = (1-\sin^2\alpha)(1+\sin^2\alpha+\sin^4\alpha) perfectly matches the right side in terms of \cos. Testing \alpha=0 on statement II gives LHS = 1 and RHS = 0, proving II is not an identity.
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