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Answer 1 · 2017-03-02T19:01:33

see below

Use the following Properties:
1. Pythagorean Identity
#1+cot^2x=csc^2x# and solve for #cot^2x#

Left Hand Side:
#cot^2x/(csc x-1)=(csc^2x-1)/(cscx-1)#

#=((csc x+1)(cscx-1))/(cscx -1)#->factor the difference of 2 squares above

#=((csc x+1)cancel((cscx-1)))/cancel((cscx -1))#

#=cscx+1#

#=1/sinx +1#

#=1/sinx+sinx/sinx#

#=(1+sinx)/sinx#

#:.=# Right Hand Side