Question

-1 / (tanx - secx) = (1+ sinx) / cosx

Answer 1

Is this an identity you are trying to prove?

Answer 2

yes It is

Answer 3

I would start out on the left side. Replace tan with sin/cos. Replace sec with 1/cos
Add the two together and then multiply numerator and denominator by cos. See where that takes you.

Answer 4

ok I got -1 over cosx/sinx - 1

Answer 5

That can't be right. If you multiply numerator and denominator by cos, the numerator will be -cos since -1 times cos is -cos

Answer 6

Oh yeah your right. ok its -cosx over sinx -1

Answer 7

Ok. Now I think I would multiply numerator and denominator by sinx + 1

Answer 8

ok I have -cosx(sinx+1) over sin^2x + 1

Answer 9

Nope. (sinx-1)(sinx+1)=sin^2-1

Answer 10

You should have:
\[\frac{-\cos x(\sin x+1)}{\sin ^2x-1}\]

Answer 11

yes your right

Answer 12

Now change -cosx to cos x and change the denominator to its opposite.

Answer 13

Then in the denominator you will have 1-sin^2x
Replace that with cos^2x and cancel cos x

Answer 14

that just leaves me sinx + 1. I need a cosx on the bottom

Answer 15

Oh nevermind its squared on the bottom

Answer 16

yep

Answer 17

I got it to equal!!! Thank you very much

Answer 18

yw