Question

Please help with Trig Identities... tried it, but continued to get stuck at the end... Prove by working one side:
(cos x/ 1+ sin x) - ( 1-sin x/ cos x)= 0

Answer 1

cos(x)/(1+sin(x)) ?? is that corrrect?

Answer 2

yes

Answer 3

id assume yes, since cos(x)/1 would be futile :)

Answer 4

add the right "term" to the right side of the (=) for starters

Answer 5

cos x 1-sin x
-------- = -------
1+sin cos

Answer 6

the RHS = sec - tan

Answer 7

not = it is -...... it equals 0

Answer 8

you should use algebraic techniques to "prove" the statement.

All I did was move -((1-sin)/cos) to the other side for the moments :)

Answer 9

if we cross multiply we get:

cos^2 = (1-sin)(1+sin)

Answer 10

i dont understand... im so confused

Answer 11

cos^2 = 1 - sin^2 which is true

Answer 12

yes

Answer 13

are you trying to just work one side and not manipulate it to your whim?

Answer 14

yes only working one side to prove the other

Answer 15

you could try decomposing fractions..... maybe if you want to try that way

Answer 16

i ended up at: (1- sin ^2 x - 1- sin x)/ cos x

Answer 17

cos 1-sin
-------- - ------- = 0
1+sin cos

ok....yeah, get like denominators and such...same thing I did pretty much:

cos^2 - (1-sin^2)
--------------- = 0
cos(1+sin)

Answer 18

now we see that cos^2 - (cos^2) = 0 so that whole thing is 0

Answer 19

do you see it?

Answer 20

yes, thank you

Answer 21

how did you get to this? (1- sin ^2 x - 1- sin x)/ cos x

Answer 22

because cos ^2 = 1 - sin ^2

Answer 23

thank you for helping me

Answer 24

youre welcome :)