Question

Verify 1/1+sinx + 1/1-sinx = 2tan^2x

Answer 1

Combine the expression on the left side of the equation, so there is one common denominator.

Answer 2

ok

so that would be 1-sinx/(1+sinx)(1-sinx) + 1+sinx/(1+sinx)(1-sinx)

now what?

Answer 3

Yes, add them together, and expand the denominator.

Answer 4

I don't know how to expand, what exactly do I do?

Answer 5

We have this so far:
\[\frac{1-sinx+1+sinx}{(1+sinx)(1-sinx)} = 2\tan^{2}x\]

Answer 6

yes

Answer 7

Simplify the numerator on the left side. FOIL the denominator.

Answer 8

so the numerator is just 2 right?

Answer 9

Yes.

Answer 10

ok so I have 2/1-sinx+sinx-sin^2x, is that right?

Answer 11

Yes, and that can be simplied even more.

Answer 12

so 1-sin2x-sin^2x?

Answer 13

for the denominator

Answer 14

Err now, the sinx 's cancel out.
You should get 1/(1-sin^2x)
Which simplies the 1/cos^2x

Answer 15

\[\frac{2}{1-\sin^2 x} = 2\tan^2x\]

\[\frac{2}{\cos^2 x} = 2\tan^2x\]

Answer 16

alright so now what? and by the way thanks for all the help.

Answer 17

I'm trying to think.
We don't want to mess with the 2tan^2x because we're proving that.

Answer 18

Hmm, this doesn't seem right at all...

Answer 19

2 sec^2 x = 2 tan^2 x
Hmm, did you type it out right?

Answer 20

ahh i'm stupid sorry it was 2+2tan^2x

Answer 21

Hmm, ok, give me a minute.

Answer 22

was all this for nothing or do we have to start over?

Answer 23

Oh, wait this is easy lol.
2 sec^2 x
2*(1 + tan^x)
2 + 2 tan^2 x :)

Answer 24

is that the entire thing or is that ending from somewhere before?

Answer 25

No, that's the entire thing. Lemme write it out nicely.

Answer 26

\[2 \sec^2 x = 2 + 2\tan^2x\]
\[2(1+\tan^2x) = 2 + 2\tan^x\]
\[2 + 2\tan^2x = 2 + 2\tan^2x\]

Answer 27

how are you getting the 2sec^2x?

Answer 28

Remember the first half that I did, and I told you I was confused?

Answer 29

\[\frac{2}{\cos^2 x} = 2\sec^2x = 2+2\tan^x\]

Answer 30

mhm, so what should I erase? i need to show all the steps

Answer 31

tan^2 x

Answer 32

ahh ok that makes sense

Answer 33

Don't erase anything. I fully proved it, you just forgot to add that 2 to the right side lol.

Answer 34

Alright, thank you very much. I have like 4 other questions so should I make a new question or put it here? If you're willing to help me.

Answer 35

Um, you should make a new question. I might help, not sure lol. Sorry.