Question

(cotθ-tanθ)/(sinθ+cosθ)=csc(θ)-sec(θ)
verify

Answer 1

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

Answer 2

\[\frac{ \cos \theta-\sin \theta }{\sin \theta \cos \theta }=\frac{ \cos \theta }{\sin \theta \cos \theta }-\frac{ \sin \theta }{ \sin \theta \cos \theta }\]
\[\frac{ 1 }{ \sin \theta }-\frac{ 1 }{ \cos \theta }=\csc \theta-\sec \theta\]

Answer 3

bingo