Abstract: The existence of sine and cosine series as a Fourier
series, their L1-convergence seems to be one of the difficult question
in theory of convergence of trigonometric series in L1-metric norm.
In the literature so far available, various authors have studied the
L1-convergence of cosine and sine trigonometric series with special
coefficients. In this paper, we present a modified cosine and sine sums
and criterion for L1-convergence of these modified sums is obtained.
Also, a necessary and sufficient condition for the L1-convergence of
the cosine and sine series is deduced as corollaries.