Discussion
What is the value of \(\sec^2 \theta - \tan^2 \theta\)?
Answer: B
This is another key Pythagorean identity. It is derived from \(\sin^2 \theta + \cos^2 \theta = 1\) by dividing the entire equation by \(\cos^2 \theta\).
\(\frac{\sin^2 \theta}{\cos^2 \theta} + \frac{\cos^2 \theta}{\cos^2 \theta} = \frac{1}{\cos^2 \theta}\)
\(\tan^2 \theta + 1 = \sec^2 \theta\)
Rearranging gives \(\sec^2 \theta - \tan^2 \theta = 1\).
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