Proving identities:

Question

1) 1+ 1/tan^2x = 1/sin^2x

2) 2sin^2 x-1 = sin^2x - cos^2x

3) 1/cosx - cosx = sin x tan x

4) sin x + tan x =tan x (1+cos x)

5) 1/1-sin^2x= 1+tan^2 x

How in the world do I prove this...please help...

I appreciateyour time thankyou soo much!!

Answer 1

There is on one correct and foolproof way to prove identities.
There are some general rules you might follow
1. look for obvious relations , like sin^2 x + cos^2 x = 1
or 1 + tan^2 x = sec^2 x
-- make yourself a summary of these collected from your text or notebooks
2. usually, changing all ratios to sines and cosines often gives quick and easy results
3. start with the more complicated looking side, and try to work it towards the expression on the other side , or
4. work down one side until you can't seem to go any further, now switch to the other side and try to obtain that last expression

e.g. #4
sinx + tanx = tanx (1+cosx)

LS = sinx + sinx/cosx
= (sinxcosx + sinx)/cosx
= sinx(cosx + 1)/cosx
= (sinx/cosx)(1 + cosx)
= tanx (1 + cosx)
= RS

#2
2sin^2 x - 1 = sin^2x - cos^2x

RS = sin^2 x - (1 - sin^2 x)
= sin^2 x - 1 + sin^2 x
= 2sin^2 x - 1
= LS
well, that was an easy one

try the others by using similar methods.
come back if you get stuck.

Answer 2

My first line should have been:

There is NO one correct and foolproof way to prove identities.

Answer 3

OHHH!!! Ok thankyou soooo much I greatly appreciate your help and one compliment...Your way better than my teacher...once again thankyou sooo much I think I get the jist of it now:)