Identity Problem: 1 + cos ^2 x = 1 + sec ^2 x / 1 + tan ^2 x

[baseballboy]

I am having problems figuring this out. Your help would be greatly appreciated!!
1 + cos ^2 x = 1 + sec ^2 x / 1 + tan ^2 x


Thank you!

 

[ksdhart]

The first thing I'd note is that grouping symbols are very important. You need to use them, in order to clearly communicate what you mean. In this case, I can guess that because you said you titled your post "Identity Problem," that the (unposted) instructions were something like "Prove the following is an identity." What you wrote is equal to the following, which is not an identity:

\(\displaystyle 1+cos^2\left(x\right)=1+\frac{sec^2\left(x\right)}{1}+tan^2\left(x\right)\)

What I'm pretty sure you meant is this, which is an identity: 1 + cos^2(x) = [1+cos^2(x)]/[1+tan^2(x)]

\(\displaystyle 1+cos^2\left(x\right)=\frac{1+sec^2\left(x\right)}{1+tan^2\left(x\right)}\)

That said, my actual advice for solving the problem is to recall the fundamental identities you already know. Start with the right-hand side of the equation. I see 1 + tan^2(x). Do you know an identity for this value? If not, try writing tan^2(x) is terms of sin^2(x) and cos^2(x), then manipulate the fractions until you see it. Once you make the appropriate substitution for 1+tan^2(x), simplify the resulting fraction.

 

[baseballboy]

I am having problems figuring this out. Your help would be greatly appreciated!!
1 + cos ^2 x = 1 + sec ^2 x / 1 + tan ^2 x


Thank you!

"I have been working on this problem for awhile. Is the answer NO RESULT? Please help.....thank you

 

[stapel]

"I have been working on this problem for awhile. Is the answer NO RESULT? Please help.....thank you

I'm sorry that you were unable to view the reply. It stated the following:

The first thing I'd note is that grouping symbols are very important. You need to use them, in order to clearly communicate what you mean. In this case, I can guess that because you said you titled your post "Identity Problem," that the (unposted) instructions were something like "Prove the following is an identity." What you wrote is equal to the following, which is not an identity:

\(\displaystyle 1+cos^2\left(x\right)=1+\frac{sec^2\left(x\right)}{1}+tan^2\left(x\right)\)

What I'm pretty sure you meant is this, which is an identity: 1 + cos^2(x) = [1+cos^2(x)]/[1+tan^2(x)]

\(\displaystyle 1+cos^2\left(x\right)=\frac{1+sec^2\left(x\right)}{1+tan^2\left(x\right)}\)

That said, my actual advice for solving the problem is to recall the fundamental identities you already know. Start with the right-hand side of the equation. I see 1 + tan^2(x). Do you know an identity for this value? If not, try writing tan^2(x) is terms of sin^2(x) and cos^2(x), then manipulate the fractions until you see it. Once you make the appropriate substitution for 1+tan^2(x), simplify the resulting fraction.

So, my question to you is: Did the helper correctly guess your meaning? If not, please post corrections. If so, please confirm.

When you reply, please include a clear listing of at least one of your efforts (since you've "been working on this problem for awhile" now), showing all of your steps and reasoning, so we can see where things are bogging down. Thank you!