What is cottheta-costheta in terms of sintheta?

1 Answer
Dec 6, 2015

[(1 - sin(x))^(3/2)sqrt(1 + sin(x))]/(sin(x))

Explanation:

We first have to put everything at the same denominator.

cos(x)/sin(x) - cos(x) = (cos(x) - sin(x).cos(x))/(sin(x)) = [(cos(x))(1 - sin(x))]/(sin(x))

We know that :
cos(x) = sqrt(1 - sin^2(x)) = sqrt(1 - sin(x))sqrt(1 + sin(x)).

Therefor,
cot(x) - cos(x) = [(1 - sin(x))^(3/2)sqrt(1 + sin(x))]/(sin(x))