Question #cf786

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Answer 1 · 2017-03-02T23:00:33

see below

Use the following Properties:

Left hand Side :

#(1-cotx)^2 + (1-tan x)^2=1-2cotx+cot^2x+1-2tan^2x+tan^2x#

#=1+cot^2x-2cotx-2tanx+1+tan^2x#

#=csc^2x-2(cotx+tanx)+sec^2x#

#=csc^2x-2(cosx/sinx+sinx/cosx)+sec^2x#

#=csc^2x-2((cos^2x+sin^2x)/(sinx cosx))+sec^2x#

#=csc^2x-2(1/(sinx cosx))+sec^2x#

#=csc^2x-2(1/sinx 1/cosx)+sec^2x#

#=csc^2x-2 1/sinx 1/cosx+sec^2x#

#=csc^2x-2 cscx sec x+sec^2x#---> factor

#=(cscx-secx)(cscx-secx)#

#=(cscx-secx)^2#

#:.=# Right Hand Side