Question

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

Answer 1

quotent rule

Answer 2

/?

Answer 3

yeah I ment quotient rule, my bad

Answer 4

its wrong wait

Answer 5

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

Answer 6

you always have to square the denominator don't forget

Answer 7

yeah but we have to simplify using the trig identities

Answer 8

oh

Answer 9

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

Answer 10

yeah so I'm still uncertain

Answer 11

how did you get that @zarkon?

Answer 12

just simplify alvinstifla's solution

Answer 13

how exactly? please show me steps.

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

yes..you can say it that way

Answer 19

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?

Answer 20

Please go through it.