Math Help - Identity? issues

1. Identity? issues

Simplify and write the trigonometric expression in terms of sine and cosine:

?

So I came up with this
= 1/f(u)

But I am not sure what to do or if I am right?

2. Re: Identity? issues

I believe what you being asked to do is:

$\tan(u)+\cot(u)=\frac{\sin(u)}{\cos(u)}+\frac{\cos (u)}{\sin(u)}=?=\frac{1}{f(u)}$

Where the "?" is, combine terms, and you will get the desired form.

3. Re: Identity? issues

Can you explain what cofunction identities are?

4. Re: Identity? issues

Basically, if you have two complementary angles $\alpha$ and $\beta$, i.e.:

$\alpha+\beta=\frac{\pi}{2}$

then a trig. function whose argument is one of the angles will be equal to its co-function evaluated at the other. That is:

$\sin(\alpha)=\cos(\beta)$

$\cos(\alpha)=\sin(\beta)$

$\tan(\alpha)=\cot(\beta)$

$\cot(\alpha)=\tan(\beta)$

$\sec(\alpha)=\csc(\beta)$

$\csc(\alpha)=\sec(\beta)$

5. Re: Identity? issues

Originally Posted by MarkFL2
I believe what you being asked to do is:

$\tan(u)+\cot(u)=\frac{\sin(u)}{\cos(u)}+\frac{\cos (u)}{\sin(u)}=?=\frac{1}{f(u)}$

Where the "?" is, combine terms, and you will get the desired form.
Oh does this work out to Sin^2(u)+Cos^2(u) which would equal 1?

6. Re: Identity? issues

Yes, that would be the numerator...what is the common denominator, which is what f(u) is?

7. Re: Identity? issues

Originally Posted by MarkFL2
Yes, that would be the numerator...what is the common denominator, which is what f(u) is?
I am not understanding this ? if I found the numerator to be 1 this means 1=1/f(u)?

8. Re: Identity? issues

When you combine the two terms, the numerator simplifies to 1, but there is also the denominator.

9. Re: Identity? issues

I really don't know I am now lost.. I understand what you said, I just can't wrap my mind around this one...

10. Re: Identity? issues

$\frac{\sin{u}}{\cos{u}} + \frac{\cos{u}}{\sin{u}} = \frac{\sin^2{u}+\cos^2{u}}{\sin{u}\cos{u}} = \frac{1}{\sin{u}\cos{u}}$

11. Re: Identity? issues

Originally Posted by skeeter
$\frac{\sin{u}}{\cos{u}} + \frac{\cos{u}}{\sin{u}} = \frac{\sin^2{u}+\cos^2{u}}{\sin{u}\cos{u}} = \frac{1}{\sin{u}\cos{u}}$
I know my biggest problem is my algebra skill set is very poor right now.... Can you break this down into a few more steps for me to be able to understand even better?

12. Re: Identity? issues

$\frac{a}{b} + \frac{b}{a}$

common denominator is $a \cdot b$

$\frac{a \cdot a}{a \cdot b} + \frac{b \cdot b}{a \cdot b}$

$\frac{a^2}{ab} + \frac{b^2}{ab}$

$\frac{a^2+b^2}{ab}$