Question

cos^2 x + sin^2 x/cot^2 x - csc^2 x
a. csc x
b. -1
c. 1
d. sec x
I've been having trouble with this problem for 20 minutes now and every time I get an answer it's not one of the available options to pick from. Can someone please explain this?

Answer 1

the numerator is one

Answer 2

\[\cos^{2}x + \sin^{2}x = 1\]

Answer 3

\[\cot^{x}x - \csc^{2}x = -1\]

Answer 4

and if you divide everything in the equation
\[\cos^2(x)+\sin^2(x)=1\] by \[\sin^2(x)\] you will get an expression involving \(\cot^2(x)\) and \(\csc^2(x)\)

Answer 5

in fact you will get
\[\cot^2(x)+1=\csc^2(x)\]

Answer 6

so the answer is -1?

Answer 7

yes

Answer 8

okay that makes A LOT more sense now, thank you!