Question

How do I do this trigonometric identity question?

Answer 1

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

Answer 2

So I think I have step one figured out, but I got stuck here. \[\frac{ \cos x(1+\sin x) - \cos x(1- \sin x)}{1- \sin^{2}x}\]

Answer 3

yes..go ahead

Answer 4

So do I simply multiply the top next?

Answer 5

yes

Answer 6

now simplify numerator and use sin^2 + cos^2 = 1 in denominator

Answer 7

okay so is the top \[\frac{ \cos x + \cos x \sin x + \cos x - \cos x \sin x}{ cox^{2}x }\]?

Answer 8

you have the signs wrong

Answer 9

should be +,-,+

Answer 10

sign mistake..check below

Answer 11

Oh right. I see, whoops.

Answer 12

What do I do next? I can't find the next relationship.

Answer 13

what have u got?

Answer 14

\[\frac{ \cos x + \cos x \sin x - \cos x + \cos x \sin x }{ \cos^{2}x }\]

Answer 15

Ohh. I see now. so the cos x cancels out the other cos x, and thus I'm left with 2 sin x cos x? On the top?

Answer 16

it would have been better to let you work that out.
the cos x on the numerator cancels out with the cos^2(x) on the denominator
leaving 2sinx on the top and cos x on the bottom

Answer 17

@alekos Oh I was asking about the step before that last step

Answer 18

yes the top line has cosx - cosx = 0

Answer 19

I see now. I was constantly treating cos/sine/tan like numbers. -.- Thanks! Wish I could give you a medal!

Answer 20

no worries