Prove the identity: tan x - 1/ tan x + 1 = 1 - cot x/ 1 + cot x?

Question

Prove the identity: tan x - 1/ tan x + 1 = 1 - cot x/ 1 + cot x

Answer 1

If we assume tanx=y
==> cotx=1/y
==>(y-1)/(y+1)=(1-1/y)/(1+1/y)
1-1/y=(y-1)/y
1+1/y=(y+1)/y
==>
(1-1/y)/(1+1/y)=
((y-1)/y)/((y+1)/y)
((y-1)*y)/((y+1)*y)
=(y-1)/(y+1)
so both sides are equal

Answer 2

you mean (tan x-1)/(tan x+1) = (1-cot x)/(1+cot x)
lhs
= (1/cot x - 1)/(1/cot x + 1)
= ((1-cotx)/cotx)/((1+cot x)/cotx))
= (1-cot x)/(1+cot x)
= rhs
proved

Answer 3

per chance i'd be able to get you all started my innovations are frequently for algebra its merely that likely I see something (a million+tanx) / (a million+cotx) = (a million-tanx) / (cotx-a million) the right denominator a million/(cotx-a million)=a million/(-a million+cotx)= -a million/(a million-cotx) so (a million-tanx)/(cotx-a million)= -(a million-tanx)/(a million-cotx) will provide you (a million+tanx) / (a million+cotx)= -(a million-tanx)/(a million-cotx) you could now make the denominators into 'replace of squares' left element (a million+tanx)/(a million+cotx)*(a million-cotx)/(a million-cotx)=(a million..... incredible side -(a million-tanx)/(a million-cotx)*(a million+cotx)/(a million+cotx)= -(a million-tanx)(a million+cotx)/(a million-cotx^2) the (a million-cotx^2)'s cancel leaving (a million+tanx)(a million-cotx)= -(a million-tanx)(a million+cotx) likely you could take it from there? maximum proper reliable fortune

Answer 4

ya right do your own homework