 # Problem with Trig Identity

Hi,

I can't seem to prove the following trig identity, or where to start. Any ideas?

Thanks!
TrigIdentity.jpg
Math / Science Last Comment
d-glitch

8/22/2022 - Mon
d-glitch

Start by replacing tan and cot with their sin and cos equivalents.
This should be  a four line proof.
Computer Guy

So  1+sin/cos would = cos * sin/cos
d-glitch

>>  So  1+sin/cos would = cos * sin/cos

That is not true, nor one of the steps.

You have to methodically transform the Left-Hand-Side of the equation until it matches the right.

Half of the first step is to replace   1 + tan    with    1 + sin/cos
Computer Guy

Woops, that part I knew.

I mean to say that

(cos/1)/(1+(sin/cos)) where the 1's and the cos cancel out left with sinx for the first part, right?
d-glitch

After the first step, you will still have two terms on the LHS

One of them will be     cos / (1 + sin/cos)       The other will be similar.
But there is nothing to cancel out yet.
The two terms have to simplified [ Step 2]
Then combined [ Step 3]
At this point, you will be able to factor and cancel [ Step 4]
Computer Guy

Not sure how to simplify them.
d-glitch

The problem with this term   cos / (1 + sin/cos)   is that there is a fraction in the denominator.
How do you simplify that?

If the term were   3 / (1 + 2/7)  what would you do?
d-glitch

I don't imagine that this identity is particularly useful, but it is quite simple.

The only trig you need to know is that   tan = sin/cos   and   cot = cos/sin
The rest is simple algebra.

The way to solve this is to assume that it is solvable and plug away.  It is really a 60 second problem.
Computer Guy