To solve this equation, we need to use trigonometric identities. In this case, we will use the identity involving the tangent function:
1 + tan^2x = sec^2x
Therefore, the equation is equal to sec^2x. The secant function, sec(x), is defined as the reciprocal of the cosine function, so sec(x) = 1/cos(x).
Hence, the simplified expression for 1 + tan^2x is sec^2x or (1/cos^2x).
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