Question

Prove: 1+sinx/1-sinx=csc^2x+2cscx+1

Answer 1

Please Help! It's really important

Answer 2

Welcome to Openstudy

Answer 3

Just remember that \(\mathbb {cscx=\frac{1}{sinx}}\) and use \((a-b)(a+b)=a^2-b^2\)

Answer 4

is the proof solvable because iv'e tried everything?

Answer 5

if you mean
(1+sinx)/(1-sinx)=csc^2x+2cscx+1
this is not an identity. It is true for specific values of x i.e. you can solve for the x's that make it true.

Answer 6

how could i solve for x

Answer 7

Up above you said Prove:
Is this supposed to be an identity that they want you to prove ?
(though it's not an identity, this may be a question with a "typo" and they meant to give an identity)

Answer 8

Or do they want you to "solve for x" ?

Answer 9

It's supposed to be a trig identity that he wants us to prove

Answer 10

I have been trying for hours to prove it

Answer 11

I tried and found out that this is not an identity. @phi is right

Answer 12

If the right side is \(sec^2x+2secx+1\), then it will be an identity. Is that right, @phi?

Answer 13

no, I don't think its sec^2 + 2sec + 1 (but if you can show it works, I'm all ears)
I'm trying to figure out what they might have meant, but so far, no luck.

Answer 14

I will try

Answer 15

First, is it really
\[ \frac{1+\sin x}{1-\sin x}= \csc^2 x+2\csc x+1\]?

Answer 16

It says, PROVE: you can manipulate the left side to make it 'look' like the right side. Do not manipulate the right side.

Answer 17

yes that is what the question is

Answer 18

what do you get if you let x=30 degrees for both sides ?

Answer 19

Yeah, @phi is right. Neither way is an identity

Answer 20

sin(30)= 0.5
(1+0.5)/(1-0.5) = 3

csc(x)= 1/sin(x)
so csc(30) = 2
csc^2(30)= 4

the right side is csc^2(30) + 2 csc(30) + 1 = 4 +2 +1 = 7
3 does not equal 7

that proves it's not an identity

Answer 21

Okay! Thank you so much for your help!

Answer 22

**the right side is csc^2(30) + 2 csc(30) + 1 = 4 +2*2 +1 = 9
3 does not equal 9 that proves it's not an identity

Answer 23

It's just weird that he would ask that question!

Answer 24

so it might be a "mistake" or he wanted you to show it's not true.