Question

integral of 1/(cos (x) -1)

Answer 1

can we rewrite this as

secx-1

Answer 2

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

Answer 3

\[-\int\limits_{}^{}\frac{\cos(x)}{\sin^2(x)} dx-\int\limits_{}^{}\frac{1}{\frac{1}{2}(1-\cos(2x)} dx\]

Answer 4

for the first one let u=sin(x)
let me know if you need more help

Answer 5

oh, nice job myin, multiplying by the conjugate

Answer 6

how do you know this???

Answer 7

so what is the actual answer?

Answer 8

and just to show off a little if you want
\[\int\frac{1}{-\sin^2(x)}dx\] i would just recall that this is
\[-\int\csc^2(x)dx\] so that the integrand is instantly the derivative of
\[\cot(x)\]

Answer 9

i get an actual answer of
\[\csc(x)+\cot(x)\]

Answer 10

that is the actual answer

Answer 11

in actuality

Answer 12

how do i know this?

Answer 13

that was my question. it was a serious one. i would never know to do this

Answer 14

well i wanted to get the bottom as one term
so i can break it up

Answer 15

although i have to say i like my method of solving
\[-\int\frac{1}{\sin^2(x)}dx\]

Answer 16

yes i wasn't thinking there

Answer 17

ah that makes sense.

Answer 18

also might explain why we see all those trig problems that say "show
\[\frac{\sin(x)}{1+\cos(x)}=\text{whatever}\]

Answer 19

oh yes identities

Answer 20

it can be useful in trig

Answer 21

i mean in calc

Answer 22

guess they prove useful later. only problem is it is two semesters later so they forget

Answer 23

right

Answer 24

some people don't even take trig

Answer 25

same as those problems that say find
\[\tan(\sin^{-1}(x))\] by the time they see it again it is in calc 2

Answer 26

i love those problems

Answer 27

i know you do. actually i do too

Answer 28

i was like telling my trig students make sure you know how to do these i love these

Answer 29

try to explain as best i can that is it exactly the same as those problems that say "find the other trig functions of theta if sin(theta) = whatever

Answer 30

thats key for its gonna be on the test

Answer 31

ti 89 does it symbolically.

Answer 32

lol
ok gnight

Answer 33

goodnight