How do you verify the identity $csc(-x)/sec(-x)=-cotx$ ?

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Answer 1 · 2017-01-18T15:55:33

see below

Left Hand Side:

Use the even and odd properties for trigonometric functions.
$sin(-x)=-sinx and cos(-x)=cosx$

$csc(-x)/sec(-x) = (1/sin(-x))/(1/cos(-x))$

$=1/-sinx * cosx/1$

$=cosx/-sinx$

$=-cot x$

$:.=$ Right Hand Side

How do you verify the identity csc(-x)/sec(-x)=-cotxcsc(-x)/sec(-x)=-cotx?