How do you prove #(1-cos(x)) / sin(x) = csc(x) - cot(x) #?

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Answer 1 · 2016-04-30T00:46:59

Recall the following identities:

#1. color(red)(cscx=1/sinx)#

#2. color(blue)(cotx=cosx/sinx)#

Given,

#(1-cosx)/sinx=cscx-cotx#

Simplify the right side.

#color(red)(cscx)-color(blue)(cotx)#

#=color(red)(1/sinx)-color(blue)(cosx/sinx)#

#=(1-cosx)/sinx#

#:.#, LS#=#RS.