Reduce the given expression to a single trigonometric function

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1
1 + sin t
 + 
1
1 − sin t
Oct 12th, 2015

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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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Oct 12th, 2015

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