# Thread: Basic trigonometric identities problem?

1. ## Basic trigonometric identities problem?

Can anyone show me how to do this problem?
1+cot^2x-cos^2x-cos^2xcotx^2
This if how far I have gotten

cscx^2-cos^2x-cos^2x (cosx^2/sinx^2)

(1/sinx^2)-cos^2x-cos^2x(cosx^2/sinx^2)

I am not sure how to proceed unfortunately?

2. What are you trying to show that it is equivalent to?

3. I am supposed to simplify it as much as possible.

4. Get everything to have a common denominator of $\displaystyle \sin^2{x}$ and simplify the numerator...

5. Originally Posted by homeylova223
Can anyone show me how to do this problem?
1+cot^2x-cos^2x-cos^2xcotx^2
$1+\cot^2{x}-\cos^2{x}-\cos^2{x}\cot^2{x}$

$1+\cot^2{x}-\cos^2{x}(1 + \cot^2{x})$

$(1+\cot^2{x})(1 - \cos^2{x})$

$\csc^2{x} \cdot \sin^2{x} = 1$

6. I have another trigonometric identities I need some help in although I do not want to start a new thread. It is similar.

cos^4x+2cos^2xsin^2x+sin^4x I need to simplify it this is what I have done thus far
Factor cos^2x
cos^2x+2sin^2x+sin^4x factor out sin^2x
then I get this cos^2x+2+sin^2x But I do not think this is right?

7. Originally Posted by homeylova223
I have another trigonometric identities I need some help in although I do not want to start a new thread. It is similar.

cos^4x+2cos^2xsin^2x+sin^4x I need to simplify it this is what I have done thus far
Factor cos^2x
cos^2x+2sin^2x+sin^4x factor out sin^2x
then I get this cos^2x+2+sin^2x But I do not think this is right?
$\cos^4{x}+2\cos^2{x}\sin^2{x}+\sin^4{x} = (\cos^2{x} + \sin^2{x})^2 =$ ???

8. Oh it is one.