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