I am trying to learn how to transform identities of one side of the equation to the other side. is this correct?
I am using 0 for theta
theta = 0
question:
tan 0 + cot 0
-------------- = csc^2 0
tan 0
answer:
cot 0 = csc 0
that answer is wrong. how does that prove an identity. you must show the left hand side and right hand side are the same. so you must turn one side into the other or bring both sides to the same thing
consider the left hand side (it is more complicated and so gives us more options to change things)
note, $\displaystyle \frac {\tan \theta + \cot \theta}{\tan \theta} = \frac {\tan \theta}{\tan \theta} + \frac {\cot \theta}{\tan \theta}$
now what?
huh??
lets not lose sight of the objective here. we are proving an identity. we are trying to turn one side into the other. your objective is to turn $\displaystyle \frac {\tan \theta}{\tan \theta} + \frac {\cot \theta}{\tan \theta}$ into $\displaystyle \csc^2 \theta$ through simplification. that will show that the left hand side and right hand side are the same
I'm going to work this out for you since it seems you are a little lost and hopefully me working it will help you understand, but I what you to come back and explain the steps I did so you will learn.
$\displaystyle \frac {\tan \theta + \cot \theta}{\tan \theta}$
$\displaystyle =~\frac {\tan \theta}{\tan \theta} + \frac {\cot \theta}{\tan \theta}$
$\displaystyle = 1+ \frac{cos^2\theta}{sin^2\theta}$
$\displaystyle = \frac{sin^2\theta}{sin^2\theta} + \frac{cos^2\theta}{sin^2\theta}$
$\displaystyle =~\frac{1}{sin^2\theta}$
$\displaystyle =~csc^2\theta$
evidently you need help with adding fractions (see posts #3, 9 and 11 here). you cannot cancel like that! and you cannot have sin and cos by themselves, write sin(x) and cos(x) or something
furthermore, as i said, you are proving an identity. if you don't end up with something that looks like the other side, you are wrong
you're asking us or telling us?this is how I am thinking about it?
11rdc11 did the problem for you. make sure you follow what he did
yes, i know. i was messing with you because you put a question mark at the end.
study what 11rdc11 did and make sure you have no questions. then, make sure you review fractions and trig identities. things like $\displaystyle \sin^2 \theta + \cos^2 \theta = 1$, stuff like that you should know by heart. you are in for a LOT of pain if you do not get these basic things. you don't want to be one of those students that end up in calculus and can't do basic algebra, trust me