1 + tan^2 x
To simplify the expression 1 + tan^2(x), we can use the trigonometric identity: tan^2(x) + 1 = sec^2(x)
To simplify the expression 1 + tan^2(x), we can use the trigonometric identity: tan^2(x) + 1 = sec^2(x).
The trigonometric identity tan^2(x) + 1 = sec^2(x) is derived from the Pythagorean identity for the tangent function, which states: tan^2(x) + 1 = 1/cos^2(x).
So, to simplify the expression 1 + tan^2(x), we can rewrite it as sec^2(x).
Therefore, 1 + tan^2(x) simplifies to sec^2(x).
Note: The identity tan^2(x) + 1 = sec^2(x) is valid for all values of x, except for those where cos(x) = 0, as division by zero is undefined.
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