Trig Question: if f(x)=sec(x) and if tan(x)=1 what is the value of (f*f)(x) ?

[MJFan]

Hi!
Here is the question:
if f(x)=sec(x) and if tan(x)=1 what is the value of (f*f)(x)

Currently I have only got this:

The teacher mentioned that we are supposed to get a numerical value to the answer of this, I'm just not sure how to get that.
Any help is appreciated!

 

[Deleted member 4993]

Hi!
Here is the question:
if f(x)=sec(x) and if tan(x)=1 what is the value of (f*f)(x)

Currently I have only got this:

The teacher mentioned that we are supposed to get a numerical value to the answer of this, I'm just not sure how to get that.
Any help is appreciated!

What does (f*f)(x) mean to you (according to your textbook or class notes)?

 

[MJFan]

What does (f*f)(x) mean to you (according to your textbook or class notes)?

It means that you take one function and multiply it with the other. e.g. f(x)=x-2 and g(x)=x+3 and if you were asked to solve (fg)(x) you would do (x-2)(x+3)=x^2+x-6

 

[pka]

Here is the question: if f(x)=sec(x) and if tan(x)=1 what is the value of (f*f)(x)
Currently I have only got this:

Your second and third lines are wrong [on the right-hand side].
$\displaystyle \sec^2(x)=1+\tan^2(x)$

 

[MJFan]

Your second and third lines are completely wrong.
$\displaystyle \sec^2(x)=1+\tan^2(x)$

Just wondering, how did you arrive at the tan^2(x)?

 

[ksdhart2]

Just wondering, how did you arrive at the tan^2(x)?

That's just one of the very well known identities that you'd do well to memorize and put in your "tool kit." It can be derived quite easily from the Pythagorean Identityhttp://www.purplemath.com/modules/idents.htm#basic. Start with:

$\displaystyle sin^2(\theta)+cos^2(\theta)=1$

What happens if you divide through by $\displaystyle cos^2(\theta)$? Where does that lead? Can you see how that helps prove the above identity?