1 + tan^2(x)
To simplify the expression 1 + tan^2(x), we will use the trigonometric identity: tan^2(x) + 1 = sec^2(x)
To simplify the expression 1 + tan^2(x), we will use the trigonometric identity: tan^2(x) + 1 = sec^2(x). By rearranging this identity, we can solve for tan^2(x): tan^2(x) = sec^2(x) – 1.
Therefore, 1 + tan^2(x) = 1 + (sec^2(x) – 1).
Simplifying further, we have: 1 + tan^2(x) = sec^2(x).
Hence, the simplified expression for 1 + tan^2(x) is sec^2(x).
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