Hi there. I just learnt trigonometry today, and the teacher didn't really delve much into the topic yet, just the basic identities. I can prove these identities using normal maths rules, but not using the LHS /RHS rule as compared to what the teacher has taught us. For example;
cosec x - cot x = (sin x)/(1 + cos x) ----- (1)
cosec x - cot x = 1/(sin x) - (cos x)/(sin x)
= (1 - cos x)/(sin x) ------(2)
(sin x)/(1 + cos x) = (1 - cos x)/(sin x)
sin^2 x= 1 - cos^2 x [Basic Identity]
That is what I do to these sort of identites involving linear equations. I have no prob. doing say (sin x)/(cos x - sin x) = cot x + 1
So, can anyone post some steps for proving this? Or is my method the only way? I'm sure there's a more elegant sol.
(tan x + sec x - 1)/(tan x - sec x +1) = tan x +sec x
Since (1) = (2) . . . . No!
We can not assume that (1) = (2) . . .
. . In fact, that is what we're trying to prove.
The accepted rule for Proving Identies is: work on one side only
. . and show that it equals the other side.
There are those who disagree (some are teachers!),
. . but this is the safest approach to identities.
Your work to that point is correct: .
Now we pull a strange trick . . . multiply by
. . . .
Thanks for all the anwsers. Presumablkbly, is taken from the basic identitiy, sec^2 x = tan^2 x + 1? So I can just substitude \tan x + (\sec x - 1) in?
EDIT: Yeah. It 's only multiplying 1. Sorry I just woke up and viewed the post. Thanks to both you guys.