Question

Verify the identity and show all steps.

Answer 1

\[\cos(x)\div(1-\sin(x))=\sec(x)+\tan(x)\]

Answer 2

Try multiplying the left by 1 + sin(x):
[cos(x) + cos(x)sin(x)]/[1 - sin^2(x)]
1 - sin^2(x) = cos^2(x)
[cos(x) + cos(x)sin(x)]/[cos^2(x)]

cos(x)/cos^2(x) + cos(x)sin(x)/cos^2(x)

1/cos(x) + sin(x)/cos(x)

sec(x) + tan(x)