asked on # Problem with Trig Identity

Hi,

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

Thanks!

TrigIdentity.jpg

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

Thanks!

TrigIdentity.jpg

Math / Science

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

>> 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**

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

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?

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?

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]

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]

Not sure how to simplify them.

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?

How do you simplify that?

If the term were

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.

The only trig you need to know is that

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.

I know what tan and cot equal. I just don't know what to do with the (1+sin/cos)

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tanandcotwith theirsinandcosequivalents.This should be a four line proof.