Question

more identities <.<

Answer 1

@dude
@tranquility
@surjithayer
@AZ
@darkknight

Answer 2

@darkknight

Answer 3

\[5\csc^2x+4cscx-1= (5\csc(x)-1)(\csc(x)+1)\] just a way to rewrite the top left, we only want to work with the left side

Answer 4

kay

Answer 5

let us start on the left hand side and try to make factors of the numerator
\[\frac{ 5 \csc ^2x+4\csc x-1 }{ \cot ^2x }\]
\[\frac{ 5\csc ^2 x+5\csc x-\csc x-1 }{\csc ^2x-1 }\]
\[\csc^2x-\cot^2x=1\]
\[\cot^2x=\csc^2x-1\]

Answer 6

\[\frac{ 5\csc x(\csc x+1)-1(\csc x+1) }{(\csc x+1)(\csc x-1) }\]
\[\frac{ (\csc x+1)(5 \csc x-1) }{ (\csc x+1)(\csc x-1) }\]

Answer 7

can you solve further?

Answer 8

oh and then they cancel out

thank youuuuuuuuu

Answer 9

yes