Question

How to prove (1-secx)/(1-cosx)=-secx

Answer 1

Hello,
We suppose x ≠+/-π/2. (division by 0)


sec x=1/cos x

1-sec x= 1-1*cos x=(cos x -1)/cos x

(1-sec x)/(1-cos x)=(cos x -1)/(cos x*(1-cos x))=-1/cos x=- sec x

Answer 2

To answer, we have to simplify the expression given. We know that:

sec x=1/cos x

1-sec x= 1-1/cos x=(cos x -1)/cos x

(1-sec x)/(1-cos x)=(cos x -1)/(cos x*(1-cos x))=-1/cos x=- sec x