Can't seem to get this:
a) 1-tan x/1- cot x = - tan x
and
b) 1+ cot x/1+ tan x = cot x
1) 1-tanx/1-cotx = -tanx
Using the Left side
1-tanx/1-cotx
= 1-(sinx/cosx)/1-(cosx/sinx)
= (cosx-sinx/cosx)/(sinx-cosx/sinx)
= (cosx-sinx)sinx/-(cosx-sinx)cosx
= sinx/-cosx
= - tanx
2) 1-cotx/1-tanx = cotx
Using the Left hand side
1+cotx/1+tanx
= 1+(cosx/sinx)/1+(sinx/cosx)
= (sinx+cosx/sinx)/(cosx+sinx/cosx)
= (sinx+cosx)cosx/(sinx+cosx)sinx
= cosx/sinx
= cotx
Using the equation
tanx=sinx/cosx