Question

Express this in simplest form

Answer 1

?

Answer 2

\[\Large \tan^{-1}(\frac{cosx}{1-sinx})\]

Answer 3

given
\[\frac{-\pi}{2}<x<\frac{3\pi}{2}\]

Answer 4

please let me post my attempt first

Answer 5

Whenever I see a “Customer is always right” sign, I sit there hoping a KKK member walks through the doors.

Answer 6

yes absolutely :)

Answer 7

In the end I get
\[\LARGE \tan^{-1}(\tan(\frac{\pi}{4}+\frac{x}{2}))\]
now to check if this is true
\[\LARGE \frac{-\pi}{2}<x <\frac{3\pi}{2}\]
\[\LARGE \frac{-\pi}{4}<\frac{x}{2}<\frac{3\pi}{4}\]
\[\LARGE \frac{\pi}{4}+\frac{-\pi}{4}<\frac{\pi}{4}+\frac{x}{2}<\frac{\pi}{4}+\frac {3\pi}{4}\]
\[\LARGE0<\frac{\pi}{4}+\frac{x}{2}<\pi\]

Answer 8

since its not in the domain..

Answer 9

\[\LARGE \frac{-\pi}{2}<\frac{\pi}{4}+\frac{x}{2}-\frac{\pi}{2}<\frac{\pi}{2}\]
so answer should be that thing? in between

Answer 10

i think u r right :)\[\frac{x}{2}-\frac{\pi}{4}\]

Answer 11

but the answer says x/2+pi/4..they took it out directly :O

Answer 12

o.O

Answer 13

i mean arctan(tan(pi/4+x/2))=pi/4+x/2
answer^^

Answer 14

i know, but the range of arctan is \((-\frac{\pi}{2},\frac{\pi}{2})\) right?

Answer 15

yes!

Answer 16

so i thought the answer must be that thing up there in between :) ??

Answer 17

most probably!