How would I verify the equation:

cot^4(x)+2 cot^2(x)+1=csc^4(x)

Question

How would I verify the equation: 

cot^4(x)+2 cot^2(x)+1=csc^4(x)

anonymous · Answer

Would I factor it or attempt to?

ganeshie8 · Answer

hint :  a^2+2ab+b^2 = (a+b)^2

ganeshie8 · Answer

hint2 : 1 = 1^2

anonymous · Answer

Can I us x's in replacement of cot and replace cot later?

ganeshie8 · Answer

yes

anonymous · Answer

So the factored eq would be:$$(\cot^2\theta +1)^2=\csc^4\theta ?$$

ganeshie8 · Answer

looks good ^

anonymous · Answer

and then solve from there?

ganeshie8 · Answer

you're done ! there is nothing to solve actually :)

anonymous · Answer

wow...

ganeshie8 · Answer

just use the identity $\large 1 + \cot ^2 \theta = \csc ^2 \theta$

anonymous · Answer

Oh then use trig identities to say that^^^

ganeshie8 · Answer

$\large \cot^4(x)+2 \cot^2(x)+1$

say cot^2 = x

$\large x^2 + 2x+1$

$\large  (x+1)(x+1)$

$\large  (x+1)^2$

ganeshie8 · Answer

plugin x = cot^2 and then use the trig identity

anonymous · Answer

Thank you so much. This community is as good as a school teacher. going into college this year and am trying to remember most of the trig stuff.

ganeshie8 · Answer

$\large ( \cot^2 \theta + 1)^2$

$\large ( \csc^2\theta )^2$

$\large \csc^4 \theta$

which is same as right hand side. so we're done !

ganeshie8 · Answer

np, you're welcome :) you must be excited about the college life ! good luck !!

anonymous · Answer

ty