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Prove the following trigonometric results: (a) cot(theta)*cot(60 deg - theta)*cot(60 deg + theta) = cot(3 theta) (b) cos(5 theta) = 16 cos⁵(theta) - 20 cos³(theta) + 5 cos(theta) (c) cos20 deg * cos40 deg * cos60 deg * cos80 deg = 1/16. Which option states the correct overall result?

1. All three identities (a), (b), (c) are true.
2. Only (a) and (b) are true.
3. Only (c) is true.
4. None of the three identities is true.

Correct answer: All three identities (a), (b), (c) are true.

Solution

Each is a standard identity; the multiple-angle and product formulas verify all three.

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