Question

Simplify the expression:
1-cotx/tanx-1

Answer 1

Multiply numerator and denominator by sin(x) * cos(x), getting:

((sin(x) * cos(x)) - cos^2(x) / (((sin^2(x)) - (sin(x) * cos(x))) =

(cos(x) * (sin(x) - cos(x)))
------------------------------------
(sin(x) * (sin(x) - cos(x)))

and after you cancel the two identical terms (sin(x) - cos(x)), you have:

cos(x)
----------- = cot(x) <--------------- Answer
sin(x)