Question

prove the identity:
[(tanx)/(1-cosx) ] = [(cscx)(1+secx)]

Answer 1

\[\left(\begin{matrix}tanx \\ 1-cosx\end{matrix}\right)\] = (cscx)(1+secx)

Answer 2

rewrite tanx as sin x / cos x and simplify should help

Answer 3

[(tanx)/(1-cosx) ] = sin x / ( cos x - cos^2 x)
cscx (1 + sec x) = 1/sinx * ( 1 + 1/cosx)
= 1/sinx * ( ( cos x + 1) / cos x)
= ( cos x + 1) / sinx cos x

- i think i'm on the wrong track here!!!

Answer 4

- there is probably a simpler way to do this

Answer 5

\[\frac{tanx}{1-cosx}=cscx(1+secx)\]
\[tanx=(1+secx-cosx-cosxsecx)cscx\]
\[tanx=(secx-cosx)cscx\]
\[tanx=(\frac{1}{cosx}-cosx)cscx\]
\[tanx=(\frac{1-\cos^2x}{cosx})cscx\]
\[tanx=\frac{\sin^2x cscx}{cosx}\]
\[tanx=tanxsinxcscx\]
\[tanx=tanx\]

Answer 6

good job

Answer 7

ty