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[1/ (1+sint) ] +[1/ (1-sint)]

=[1/ (1+ sint) * ((1- sint) / (1- sint) )] +[1/ (1- sint) ((1+ sint) / (1+ sint) )]

=[(1-sint ) / (1- sin^2 t))] +[(1+sint) / (1- sin^2t) ]

=[(1-sint ) / cos^2t )] +[(1+sint) / (cos^2t ) ] as Cos^2t = 1- sin^2t

take L.C.M

=[(1-sint ) + (1+sint )/ cos^2t )]

=[(1-sint + 1+sint )/ cos^2t )]

=[(2 )/ cos^2t )]

=2 sec^2t answer as 1/cos^2t = sec^2t

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