72 Show that sin x1 cos x 1 cos x sin x for every number x t

72 Show that sin x1 cos x 1- cos x sin x for every number x that is not an integer multiple of .

Solution

sin x / ( 1 - cos x ) = ( 1 + cos x ) / sin x

manipulating left hand side

1 - cos x = ( 1 - cos^2 x ) / (1 + cos x )

1 - cos^2 x = sin^2 x

= sin x / ( sin^2 x / ( 1 + cos x )

= ( 1 + cos x ) / sin x

which is right side

so , they are equal