# Math Help - Simplify Expression

1. ## Simplify Expression

sin x / 1 + cos x + cot x

sin^2 x / 1 - cos x

sec^2 x -1 / sec^2 x

Thanks!

2. Hello,

Originally Posted by NeedHelp18
sin x / 1 + cos x + cot x

sin^2 x / 1 - cos x

sec^2 x -1 / sec^2 x

Thanks!

I guess the second one is :

$\frac{\sin^2 x}{1- \cos x}$

We know that $\sin^2 x+\cos^2 x=1 \implies \sin^2 x=1-\cos^2 x=(1-\cos x) \cdot (1+\cos x)$

So, how does it simplify ?

$\frac{\sec^2 x-1}{\sec^2 x}$ (or $\sec^2 x-\frac{1}{\sec^2 x}$ ?)

$=1-\frac{1}{\sec^2 x}=1-\cos^2 x=...$

Is the first one $\frac{\sin x}{1+\cos x}+\cot x$ or $\frac{\sin x}{1+\cos x+\cot x}$ ?

3. Originally Posted by Moo
Hello,

I guess the second one is :

$\frac{\sin^2 x}{1- \cos x}$

We know that $\sin^2 x+\cos^2 x=1 \implies \sin^2 x=1-\cos^2 x=(1-\cos x) \cdot (1+\cos x)$

So, how does it simplify ?

$\frac{\sec^2 x-1}{\sec^2 x}$ (or $\sec^2 x-\frac{1}{\sec^2 x}$ ?)

$=1-\frac{1}{\sec^2 x}=1-\cos^2 x=...$

Is the first one $\frac{\sin x}{1+\cos x}+\cot x$ or $\frac{\sin x}{1+\cos x+\cot x}$ ?
the first option
thanks

4. Originally Posted by NeedHelp18
the first option
thanks
For the third one ?

$\frac{\sin x}{1+\cos x}+\cot x=\frac{\sin x}{1+\cos x}+\frac{\cos x}{\sin x}$

$=\frac{\sin^2 x + \cos x (1+\cos x)}{\sin x(1+\cos x)}$

$=\frac{\cos x+\cos^2 x+\sin^2 x}{\sin x(1+\cos x)}$

$=\frac{\cos x+1}{\sin x(1+\cos x)}=\dots$

5. is the answer csc x

6. ( in this one arent u supposed to leave the sinx in the numerator)

i did it again and now i get sin x + cosx as the answer.

7. Originally Posted by NeedHelp18
( in this one arent u supposed to leave the sinx in the numerator)

i did it again and now i get sin x + cosx as the answer.
$=\frac{\color{red}\cos x+1}{\sin x({\color{red}1+\cos x})}$

Can you just simplify ?

The answer is indeed csc x

8. yeah but in this part, isnt the sin ^2 x is simplified to sin x so doesnt it have to be left in the numerator?

Thanks!

9. Originally Posted by NeedHelp18

yeah but in this part, isnt the sin ^2 x is simplified to sin x so doesnt it have to be left in the numerator?

Thanks!
If it was, sin(x) should be dividing the whole numerator...

Here, it simplifies because $\cos^2 x+\sin^2 x=1$

We don't want it to be more complicated

10. thanks, now i get it