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Is the following identity correct? cos(36 deg - A) cos(36 deg + A) + cos(54 deg + A) cos(54 deg - A) = cos 2A.

1. True
2. False
3. Cannot be determined
4. None of these

Correct answer: True

Solution

Both products simplify using cos(x-A)cos(x+A) = cos² x - sin² A; summing and using cos² 36 + cos² 54 = 1 gives cos 2A.

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