How do you simplify $(sec x / sin x) - (sin x / cos x)$ ?

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Answer 1 · 2016-06-21T19:01:59

$cot x$

$(sec x / sin x) - (sin x / cos x)$

create common denominator

$= (sec x cos x - sin^2 x ) / (sin x cos x)$

$= (1 - sin^2 x ) / (sin x cos x)$

$= (cos^2 x ) / (sin x cos x)$

$= (cos x ) / (sin x )$

$= cot x$

How do you simplify (sec x / sin x) - (sin x / cos x)(sec x / sin x) - (sin x / cos x)?