Question

prove that cosx / 1+sinx = 1-sinx / cosx

Answer 1

\[\frac{\cos(x)}{1+\sin(x)} \cdot \frac{1-\sin(x)}{1-\sin(x)}=\frac{\cos(x)(1-\sin(x))}{1-\sin^2(x)}\]

Answer 2

1-sin^2(x)=cos^2(x)

Answer 3

so something cancels right?

Answer 4

\[\frac{\cos(x)(1-\sin(x))}{\cos^2(x)}=\frac{1-\sin(x)}{\cos(x)}\]

Answer 5

thank you !!!