Question

help me verify: (sec(x -1)/(sin(x)sec(x))=tan(x/2)

Answer 1

\[\frac{ secx - 1 }{ (sinx)(secx) }\]
=\[\frac{ \frac{ 1 }{ cosx }-1 }{ \frac{ sinx }{ cosx }}\]
=\[\frac{ \frac{ 1-cosx }{ cosx }}{ \frac{ sinx }{ cosx } }\]
=\[\frac{ (1-cosx) }{ sinx }\]
=\[\frac{ 2[\sin(x/2)]^{2} }{ 2\sin(x/2) \cos(x/2) }=\frac{ \sin(x/2)}{ \cos(x/2)}=\tan(x/2)\]
got it???

Answer 2

thank you! would you be willing to help me with another? i have the answer for it, but i just don't know how to get to it.
it's a log expansion not a trig identity

Answer 3

k..fine