1. ## More Expressions (Answer Verification Needed)

1. sin (x) (cos^2 (x)) - sin (x)

2. sin (x) + cot (x) (cos (x))

3. (sec^2 (x) - 1) / sec^2 (x)

I only go to the part where its

(tan^2 (x)) / 1 + tan^2 (x)

i dont know what to do now..

Thank you once again

2. #3:

You got it to $\frac{tan^{2}x}{1+tan^{2}x}$

Use sin and cos:

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

$=\frac{sin^{2}x}{cos^{2}x}\cdot\frac{cos^{2}x}{sin ^{2}x+cos^{2}x}=sin^{2}x$

3. Hello, NeedHelp18!

$3)\;\;\frac{\sec^2\!x - 1}{\sec^2\!x}$

We have: . $\frac{\sec^2\!x}{\sec^2\!x} - \frac{1}{\sec^2\!x} \;\;=\;\;1-\cos^2\!x \;\;=\;\;\sin^2\!x$

4. Thank you guys.

did i get the other answers correct?

5. Originally Posted by NeedHelp18
1. sin (x) (cos^2 (x)) - sin (x)

2. sin (x) + cot (x) (cos (x))

3. (sec^2 (x) - 1) / sec^2 (x)

I only go to the part where its

(tan^2 (x)) / 1 + tan^2 (x)

i dont know what to do now..

Thank you once again

$sin(x)+cot(x)cos(x)=sin(x)+\frac{cos(x)}{sin(x)}co s(x)=sin(x)+\frac{cos^2(x)}{sin(x)}$
$=\frac{1}{sin(x)}\cdot{\left(sin^2(x)+cos^2(x)\rig ht)}=csc(x)$
$\frac{tan^2(x)}{1+tan^2(x)}=\frac{tan^2(x)}{sec^2( x)}=tan^2(x)cos^2(x)=sin^2(x)$.