Question

Steps on how to establish this identity:
(sinθ-cosθ+1)/(sinθ+cosθ-1) = (sinθ+1)/cosθ

Answer 1

What have you tried?

Answer 2

\[\frac{\sin\theta-\cos\theta+1}{\sin\theta+\cos\theta-1}=\frac{\sin\theta+1}{\cos\theta}\]

Answer 3

I tried writing it as\[\frac{ \sinθ-(\cosθ-1) }{ \sin+ (\cosθ-1) } \times \frac{ \sinθ-(\cosθ-1) }{ \sinθ-(\cosθ-1}\]

But then I realized that I was just crossing out the numerator and denominator... so now I'm stuck.

Answer 4

Yah, it is not a friendly one where something is obvious. If you want to simplify the left, the sum to product things might work, but I am going to try something else. I think I rememer seeing something like this, but not 100% sure.

Answer 5

Can you factor out a \[sin\theta -1\]?

Answer 6

OK. the start was right. It gets there.

Answer 7

It is ugly tho.

Answer 8

I'll say

Answer 9

u wanna know a silly way of doing all these problems

Answer 10

Yah, you have to multiply that all out, which eventually lets you cancel a 2 out of everything. Then there is some grouping, and some other cancelation.

Answer 11

if the integral or derivative of LHS = RHS then the 2 functions are equal argument

Answer 12

just thougght i throw that in there >_>

Answer 13

Not exactly useful for someone in trig.

Answer 14

maybe make it integral + derivative of LHS = RHS to make it more concrete

Answer 15

lol

Answer 16

Still not helpful for someone in trig

Answer 17

haha

Answer 18

i know lol but emccormick got this covered!!

Answer 19

OK. I am going to write out my version. What you started with will work. It is one o those things where it is a little messy, but it did get there. I think I have collapsed some steps, which is a no-no for a proof, so you may need to expand some back out and fill in the gaps.

Answer 20

^go @e.mccormick you got this!!!!

Answer 21

really ??

Answer 22

I dont understand why you are asking this question ....Its exactly similar to the last one we worked on !

Answer 23

I did it the same method! ^^ look above. I'm stuck!

Answer 24

why ? first of all divide by cos theta on both sides .You get the previous question , then I have worked it for you

Answer 25

rhs can be split as sec theta and tan theta

Answer 26

Well, this start does work. It makes it a bunch of algebra.

Answer 27

When confirming an Identity, you cannot work with both sides... You must choose one and get the other.

Answer 28

just do this

Answer 29

(sinθ-cosθ+1)/(sinθ+cosθ-1) divide by cos theta on numerator and denominator

Answer 30

You will see that its exactly the previous prove that question

Answer 31

However, taking on the RHS of an ID is always worth thinking about. It can be a very good solution. As long as you stick on the right... or just use it as a way of seeing things to aim for on the left, sort of a guide, there are lots of tricks that can be done.