Question

Use fundamental identities to write the first expression in terms of the second, for any acute angle θ.

cos θ, cot θ

Answer 1

cot(theta) = 1/tan(theta) = cos(theta)/sin(theta) =

cos(theta)/sqrt(1-cos^2(theta))

cot(theta) = cos(theta)/sqrt(1-cos^2(theta))
cot^2(theta)(1-cos^2(theta))=cos^2(theta)
(cot^2(theta)+1)cos^2(theta)=cot^2theta

cot(theta)/sqrt(cot^2(theta)+1)