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Find the value of (sec^(2)A-1)....

Find the value of `(sec^(2)A-1)`.

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To find the value of \( \sec^2 A - 1 \), we can follow these steps: ### Step-by-step Solution: 1. **Recall the Trigonometric Identity**: We know from trigonometric identities that: \[ \sec^2 A = 1 + \tan^2 A \] 2. **Substitute the Identity into the Expression**: We can substitute \( \sec^2 A \) in the expression \( \sec^2 A - 1 \): \[ \sec^2 A - 1 = (1 + \tan^2 A) - 1 \] 3. **Simplify the Expression**: Now, simplify the expression: \[ (1 + \tan^2 A) - 1 = \tan^2 A \] 4. **Final Result**: Therefore, the value of \( \sec^2 A - 1 \) is: \[ \tan^2 A \] ### Conclusion: The final answer is: \[ \sec^2 A - 1 = \tan^2 A \]
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