Basic trigonometric identities problem?

**homeylova223** · January 23rd 2011, 03:50 PM

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?

**Prove It** · January 23rd 2011, 03:53 PM

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

**homeylova223** · January 23rd 2011, 04:36 PM

I am supposed to simplify it as much as possible.

**Prove It** · January 23rd 2011, 04:57 PM

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

**skeeter** · January 23rd 2011, 04:57 PM

Originally Posted by homeylova223

Can anyone show me how to do this problem?
1+cot^2x-cos^2x-cos^2xcotx^2

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

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

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

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

**homeylova223** · January 24th 2011, 04:29 PM

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?

**skeeter** · January 24th 2011, 04:47 PM

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?

$\cos^4{x}+2\cos^2{x}\sin^2{x}+\sin^4{x} = (\cos^2{x} + \sin^2{x})^2 =$ ???

**homeylova223** · January 24th 2011, 05:46 PM

Oh it is one.

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