Question

Please PLEASE PLEASE HELP WILL GIVE MEDAL @Hero @whpalmer4 @satellite73 @Loser66 @AccessDenied Verify cscx+cotx^2*cscx=cscx^3

Answer 1

hey, guy, it is 1line proof.
factor csc out
csc(1+cot^2) = csc(csc^2)=csc^3 how it makes you stuck?

Answer 2

what side do I chose

Answer 3

left

Answer 4

I don't know how

Answer 5

I showed above, didn't you read?

Answer 6

oh I did not get that

Answer 7

thanks

Answer 8

If you don't remember your identities, you can do it with a few more lines by breaking everything down to the basics.
\[\csc x = \frac{1}{\sin x}\]\[\cot x = \frac{1}{\tan x} = \frac{\cos x}{\sin x}\]

\[\csc x + \cot^2 x\csc x = \csc^3 x\]\[\frac{1}{\sin x} + (\frac{\cos x}{\sin x})^2\frac{1}{\sin x} = (\frac{1}{\sin x})^3\]\[\frac{1}{\sin x} + \frac{\cos^2 x}{\sin^3 x} = \frac{1}{\sin^3 x}\]\[\frac{\sin^2x}{\sin^2x}* \frac{1}{\sin x} + \frac{\cos^2x}{\sin^3x} = \frac{1}{\sin^3x}\]\[\frac{\sin^2x + \cos^2x}{\sin^3x} = \frac{1}{\sin^3x}\] \[\sin^2x+\cos^2x=1\]so\[\frac{1}{\sin^3x} = \frac{1}{\sin^3x}\checkmark\]