Given that 
Take R.H.S side
\tan2xcosecx
\We have formula of tan2x
\
Substitute the formula of tan2x in tan2xcosecx
\


Multiply the denominator with cosx
\



Multiply the denominator with cosx
\

Now take L.H.S side
\

-sinx and +sinx will get cancelled
\
So the obtained L.H.S is not equal to R.H.S
\The given trignometric identity is in correct
\\