Question

prove 1-sinᶿ/cosᶿ=cosᶿ/1-sinᶿ...

Answer 1

is this \[1-\frac{\sin(\theta)}{\cos(\theta)}\]

Answer 2

good question, it's not true if you take the question to be \[(1- \sin)/(\cos) = \cos/(1-\sin)\]

Answer 3

yes..

Answer 4

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

Answer 5

which is not exactly what you posted but i think it is right.