Question

express cot teta in terms of sec teta

Answer 1

$using\ the\ identity\\ \\ 1+tan^2 \theta=sec^2 \theta\\ \Rightarrow tan^2 \theta=sec^2 - 1 \theta\\ \Rightarrow tan \theta= \sqrt{sec^2 \theta-1}\\ \Rightarrow \frac{1}{cot\ \theta} =\sqrt{sec^2 \theta-1}\\ \Rightarrow \boxed{cot\ \theta = \frac{1}{\sqrt{sec^2 \theta-1}} }$

Answer 2

cot theta=1/tan theta
tan theta=√sec²theta-1
cot theta=1/√sec²theta-1