Posted by Matt on Tuesday, January 31, 2012 at 2:28am.
Answered in another post.
tan ( x ) = sin ( x ) / cos ( x )
tan ( x ) + sin ( x ) =
sin ( x ) / cos ( x ) + sin ( x ) =
sin ( x ) * [ 1 / cos ( x ) + 1 ] =
sin ( x ) * [ sec ( x ) + 1 ] =
sin ( x ) * [ 1 + sec ( x )]
[ 1 + sec ( x ) ] / [ tan ( x ) + sin ( x ) ] =
[ 1 + sec ( x ) ] / [ sin ( x ) * [ 1 + sec ( x ) ] ] =
1 / sin ( x ) = cosec ( x )
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