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Establish the trigonometric identity: (sec(8A) - 1) / (sec(4A) - 1) = tan(8A) / tan(2A). Which option is correct?

1. The identity is valid (true).
2. The identity is false.
3. It holds only for A = 0.
4. It holds only for A = 45 deg.

Correct answer: The identity is valid (true).

Solution

Converting to sines and cosines and applying the half-angle and double-angle identities reduces the left side exactly to tan(8A)/tan(2A).

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