Question

(Tan x +1)/ sin x= (1+ cot x) / cos x prove

Answer 1

\[\frac{ tanx + 1 }{ sinx } =\frac{ 1+\cot x }{ \cos x }\]
now we take left hand side
LHS\[\frac{ tanx+1 }{ sinx }\]
as we know
tan x =\[\frac{ 1 }{ cotx }\]
\[\frac{ \frac{ 1 }{ cotx }+1 }{ sinx }\]
\[\frac{ \frac{ 1+cotx }{ \cot x } }{ sinx }\]\[\frac{ 1+cotx }{ cotx .sinx }\]
as cot x =cos x/sinx put above