Question

trig proof help pls

(sinx / 1 – cosx) + (sinx / 1 + cosx) = 2 csc x

Answer 1

@ganeshie8 I know you can do these, so can you help?

Answer 2

\[\frac{ \sin x }{ 1 - \cos x }\frac{ \sin x }{ 1 + \cos x } = 2 \csc x\]

Answer 3

\(\dfrac{ \sin x }{ 1 - \cos x }+\dfrac{ \sin x }{ 1 + \cos x }\)


\(\sin x\left(\dfrac{ 1 }{ 1 - \cos x }+\dfrac{ 1}{ 1 + \cos x }\right)\)


see if you can add the fractions inside the parenthesis and simplify a bit..

Answer 4

sin x (1 - sec x + 1 + sec x)
does this work???

Answer 5

sin x (1 / 2 cos x)

maybe??? @ganeshie8

Answer 6

As for your question,

SinX/(1 -- CosX) + (1 -- CosX)/SinX = 2CscX

First, we obtain a common denominator. So we multiply the first fraction by SinX, & the 2nd fraction by (1 -- CosX). We get:

(SinX*SinX)/[SinX(1 -- CosX)] + (1 -- CosX)(1 -- CosX)/[SinX(1 -- CosX)] = 2CscX

[(SinX)^2]/[SinX(1 -- CosX)] + (1 -- CosX)(1 -- CosX)/[SinX(1 -- CosX)] = 2CscX


Here we use the Related Angle Identity:

(SinX)^2 + (CosX)^2 = 1


[1 -- (CosX)^2]/[SinX(1 -- CosX)] + (1 -- CosX)(1 -- CosX)/[SinX(1 -- CosX)] = 2CscX

(1 -- CosX)(1 + CosX)/[SinX(1 -- CosX)] + (1 -- CosX)(1 -- CosX)/[SinX(1 -- CosX)] = 2CscX

(1 + CosX)/SinX + (1 -- CosX)(1 -- CosX)/[SinX(1 -- CosX)] = 2CscX

Next, we cancel the (1 -- CosX) from the 2nd fraction, as it's obviously un-necessary, we get:

(1 + CosX)/SinX + (1 -- CosX)/SinX = 2CscX

Since both fractions have the same denominator now, we add the numerators. We get:

2/SinX = 2CscX

The CosX terms obviously cancel out.

2CscX = 2CscX

Remember that CscX = 1/SinX.

Therefore, the equality holds true:

SinX/(1 -- CosX) + (1 -- CosX)/SinX = 2CscX

I sure hope that was clear & helpful enough. :) Good luck, take care, & have a great day. :)

Answer 7

one problem...

Answer 8

what is it huh :(

Answer 9

for the second fraction you are using (1 - CosX)/SinX
when it should be sin x / (1 + cos x)

Answer 10

does negating allow you to invert it?

Answer 11

yes that's the only way

Answer 12

alright, since I can do that, this problem makes a lot more sense.
Thank You!!!

Answer 13

your welcome :)

Answer 14

Hey we cannot break fractions like that @snackshack79
we need to follow some rules

Answer 15

alright

Answer 16

does mjmahmood 's explanation look alright, or is that what you are saying is wrong?

Answer 17

sorry, one question @ganeshie8
what is going on between steps one and two?

it makes sense, but I 'm not sure what you are multiplying by