trigonometry
posted by v .
how do i simplify (secx  cosx) / sinx?
i tried splitting the numerator up so that i had (secx / sinx)  (cosx / sinx)
and then i changed sec x to 1/ cosx so that i had
((1/cosx)/ sinx)  (cos x / sinx)
after that i get stuck

sec x = 1 / cos x
sec x  cos x = 1 / cos x  cos x =
1 / cos x  cos ^ 2 x / cos x = ( 1  cos ^ 2 x ) / cos x
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Remark :
1  cos ^ 2 x = sin ^ 2 x
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1 / cos x  cos ^ 2 x / cos x = ( 1  cos ^ 2 x ) / cos x = sin ^ 2 x / cos x
( sec x  cos x ) / sin x = ( sin ^ 2 x / cos x ) / sin x =
sin ^ 2 x / ( sin x * cos x ) =
sin x * sin x / ( sin x * cos x ) =
sin x / cos x = tan x
( sec x / sin x )  ( cos x / sin x ) = tan x
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