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Let Pn = cosⁿ θ + sinⁿ θ. If Pn - Pn-2 = k Pn-4, then the value of k is:
- k = 1
- k = -sin² θ cos² θ
- k = sin² θ
- k = cos² θ
Correct answer: k = -sin² θ cos² θ
Solution
The relationship Pn - Pn-2 = k Pn-4 can be derived using the identities of powers of sine and cosine, revealing that the difference between the terms is proportional to the product of sine and cosine squared, hence k = -sin² θ cos² θ.
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