Question

Simplify the expression. (Medal for whoever gets it, I'm so confused ;-;)

Answer 1

Do you have a specific expression?

Answer 2

@kewlgeek555 The picture.

Answer 3

hi,
let's starts with the numerator
\[\cos ^{2}x + \sin ^{2}x = 1\]

do you know that ?

Answer 4

\[\frac{ \cos ^{2}x + \sin ^{2} x}{ \cot ^{2}x - \csc ^{2}x }\]
\[\frac{ 1 }{ \cot ^{2}x - \csc ^{2}x }\]
\[\frac{ 1 }{ \frac{ \cos ^{2}x }{ \sin ^{2}x } - \frac{ 1 }{ \sin ^{2}x} }\]
\[\frac{ 1 }{\frac{ \cos ^{2}x - 1 }{\sin ^{2}x } }\]

hence
\[\cos ^{2}x - 1 = -\sin ^{2}x\]
then
\[\frac{ 1 }{ \frac{ \cos ^{2}x - 1 }{ \sin ^{2}x } } = \frac{ 1 }{ \frac{ -\sin ^{2} x}{ \sin ^{2}x }}\]
\[\frac{ 1 }{-1 } = -1\]

hope this will help ya!!!