Multiply by the one in the form of conjugate of the denominator over the conjugate of the denominator, i.e. 1-cos(x)/1-cos(x). In my book this gives (1-2cos(x) + cos^2(x))/(1-cos^2(x)).
prove that (cscx-cotx)^2=(1-cosx)/(1+cosx)
my steps are as follows:
LS
(cscx-cotx)^2
(1/sinx-1/tanx)^2
(1/sinx-cosx/sinx)^2
[(1-cosx)/sinx]^2
[(1-2cosx-cos^x)/sin^2x]
now what should I do to get it to equal the other side? I am stuck here