# What is #f(x) = int secx- cscx dx# if #f((5pi)/4) = 0 #?

After integration

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To find ( f(x) = \int \sec(x) - \csc(x) , dx ) when ( f\left(\frac{5\pi}{4}\right) = 0 ), we need to evaluate the integral and then solve for the constant of integration using the given condition.

[ f(x) = \int \sec(x) - \csc(x) , dx ]

[ = \ln|\sec(x) + \tan(x)| + \ln|\csc(x) - \cot(x)| + C ]

Given ( f\left(\frac{5\pi}{4}\right) = 0 ):

[ 0 = \ln|\sec\left(\frac{5\pi}{4}\right) + \tan\left(\frac{5\pi}{4}\right)| + \ln|\csc\left(\frac{5\pi}{4}\right) - \cot\left(\frac{5\pi}{4}\right)| + C ]

[ 0 = \ln|(-1) + (-1)| + \ln|(-1) - 1| + C ]

[ 0 = \ln(0) + \ln(-2) + C ]

[ 0 = \ln(0) \times (-2) + C ]

Since ( \ln(0) ) is undefined, the equation is unsolvable. Therefore, there might be a mistake in the question.

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