Question

verify the identity
sin x/ 1-cos x + sin x/ 1+cos x = 2csc x

Answer 1

find the LCM
(sinx^2+sinx-sinxcosx)/1-cosx^2

Answer 2

how did you get sin^2x?

Answer 3

\[\frac{ \sin x }{ (1-cosx)+sinx }*\frac{ 1 }{ (1-\cos^2 x)}\]\[\frac{ sinx }{(1-cosx)+sinx}*\frac{ 1 }{ \sin^2 x}\]You have to cross cancel the sin x's\[\frac{ 1 }{ (1-cosx)+sinx }*\frac{ 1 }{ \sin x }\]\[\frac{ 1 }{ [(1-cosx)+sinx]*sinx }\] and i'lllet you work from there

Answer 4

taking the sin x out frm LHS
: \[\sin x { \frac{ 1 }{ 1+\cos x } } + \sin x \frac{ 1 }{ 1- \cos x }\]
then taking sin x common and adding the fractions
\[\frac{ \sin x ( (1 + \cos x) + (1- \cos x)) }{ 1^{2} - \cos ^{2} x }\]
on forther simplification it becomes
\[\frac{ 2 }{ \sin x }\]
and finally we can write it as
2csc x = RHS