Prove (1+secx)/(tanx+sinx)=cscx

Answer 1

Answered in another post.

Answer 2

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 )