Question

show
((sec2θ-1)/(2sec2θsinθ))=sinθ

Answer 1

\[\frac{ \frac{ 1 }{ \cos 2\theta }-1 }{ 2(\frac{ 1 }{ \cos \theta })(\sin \theta) }=\sin \theta\]
Using the Identity \[\cos 2\theta = 1-2\sin ^{2} \theta\]
\[\frac{ \frac{ 1 }{ 1-2\sin^{2} \theta} -1}{ \frac{ 2\sin \theta }{ 1-2\sin^{2} \theta} }=\sin \theta\] Which can be simplified as
\[\frac{ 1-1+2\sin^{2} \theta }{ 2\sin \theta }=\sin \theta\]
\[\frac{ 2\sin^{2} \theta }{ 2\sin \theta }=\sin \theta\]

\[\sin \theta = \sin \theta\]