Prove the identity using the following rules, Algebra, reciprocal, quotient, Pythagorean, and odd/even?

Question

#csc(-x)/sec(-x)+cos(-x)/sin(-x)=-2cotx#

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Answer 1 · 2018-04-21T20:31:59

check the explanation below

#csc(-x)/sec(-x)=(1/sin(-x))/(1/cos(-x))=cos(-x)/sin(-x)# #color(green)(rarr "reciprocal"#

now substitute

#cos(-x)/sin(-x)+cos(-x)/sin(-x)=2cos(-x)/sin(-x)#

#color(blue)(sinx " is odd so "sin(-x)=-sinx"#

#color(blue)( cosx " is even so "cos(-x)=cosx#

Substitute

#=2cosx/-sinx##color(green)(rarreven and odd " functions"#

#=-2cot(x)##color(green)(rarrquoitent#

I hope this was helpful.