y=(cosx)/(1-sinx) use product rule. I got (1)/(1+sinx) but I need verification

quotent rule

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yeah I ment quotient rule, my bad

its wrong wait

(1-sinx)(-sinx)-(cosx)(-cosx)/(1-sinx)^2

you always have to square the denominator don't forget

yeah but we have to simplify using the trig identities

oh

\[\frac{1}{1-\sin(x)}\]

yeah so I'm still uncertain

how did you get that @zarkon?

just simplify alvinstifla's solution

how exactly? please show me steps.

\[\frac{(1-\sin(x))(-\sin(x))-(\cos(x))(-\cos(x))}{(1-\sin(x))^2}\] \[=\frac{-\sin(x)+\sin^2(x)+\cos^2(x)}{(1-\sin(x))^2}\] \[=\frac{-\sin(x)+1}{(1-\sin(x))^2}\] \[=\frac{1-\sin(x)}{(1-\sin(x))^2}\] \[=\frac{1}{1-\sin(x)}\]

so how did you end up having 1-sinx as the denominator?

\[\frac{a}{a^2}=\frac{1}{a}\]

oh okay so you had (1-sinx)/(1-sinx)(1-sinx) and you cancelled (1-sinx) out to leave you with (1-sinx( right

yes..you can say it that way

sorry I had some brain fart or something. For some reason I was changing the signs. Thank you lots Zarkon! do you think you can help me on one more problem?

Please go through it.

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