Which of the expressions given below has the same value as that of \(\cos^{2}\theta + \sin^{2}\theta\)?
\(1+\tan^{2}\theta + (1-\sec^{2}\theta)\)
By the fundamental identity, \(\cos^{2}\theta + \sin^{2}\theta = 1\). So we need the option equal to 1.
Use \(1+\tan^{2}\theta = \sec^{2}\theta\).
Option 4: \((1+\tan^{2}\theta) + (1-\sec^{2}\theta) = \sec^{2}\theta + 1 - \sec^{2}\theta = 1\).
Hence, the expression equal to \(\cos^{2}\theta + \sin^{2}\theta\) is \(1+\tan^{2}\theta + (1-\sec^{2}\theta)\).
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