Question

Prove.
(1-tanx)(1-cotx)=2-secxcscx

Answer 1

(1-tanx)(1-cotx)=1-cotx-tanx+1=2-(cotx+tanx)=2-((cosx/sinx)+(sinx/cosx))=2-(1/sinxcosx)=2-secxcscx

Answer 2

so you factored first?

Answer 3

http://en.wikipedia.org/wiki/Distributive_property
\[(1-\tan x)(1-\cot x)=1-\cot x-\tan x+1=2-(\cot x+\tan x)=2-[(\frac{ \cos x }{ \sin x })+(\frac{ \sin x }{ \cos x })]=2-(\frac{ \cos ^{2}x +\sin ^{2}x}{ sinxcosx })=2-(cscx)(secx)\]