Question

1 1 tan x
______ - ______ = 2 _____
1-sin x 1+sin x cos x

Answer 1

you want to verify this identity?

Answer 2

yes ..or 'prove' it if thats what you mean

Answer 3

yup

Answer 4

LHS = 1+ sinx - (1 - sinx) 2 sin x
---------------- = -------
1 - sin^2 x 1 - sin^2 x

now if you use the identities sin^x + cos^2x = 1
and tan x = sin x / cos x
you can get the RHS

Answer 5

the way we gotta do it in class is pick one side and make it look like the other, we cant change both

Answer 6

i got up to 1 + sin x - (1 - sin x)
--------------------
cos ^2 x

Answer 7

but i dont know what to do next...

Answer 8

next simplify the numerator

Answer 9

how?

Answer 10

well its just simple algebra - remove brackets to get 1 + sin x - 1 + sin x
what does that give?

Answer 11

the 1's are eliminated right?

Answer 12

2sin x?

Answer 13

yes

Answer 14

so you have 2 sin x
-----
cos^2 x

now sinx / cos x = tan x so .....

Answer 15

divide one sin from the numerator with one cos from the denominator to get