Trig
posted by Matt on .
Prove (1+secx)/(tanx+sinx)=cscx

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 )