(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

12cot^{2}(2x)=4

(8 exact answers)

3cos^{2}(3x)=2sin(3x)

(6 decimal answers)

cos(3x)=sec(3x)+2tan^{2}(3x)

(6 exact answers) hint(get all cosines) <- teacher wrote that

And then I have to prove by working on one side:

sin^{3}(x) / 1-cosx = sinx*cosx+sinx

and

(sinx / cosx-1) + (sinx / cosx+1) = 2cosx / -sinx

2. Relevant equations

sin^{^2}x + cos^{2}x = 1 (and the other forms)

1+cot^{2}x = csc^{2}x

1+tan^{2}x = sec^{2}x

I can only use these forumulas, however you can rearrange the forumlas

3. The attempt at a solution

There were other problems of the prove by working on one side that I was able to figure out, so just a few beginning steps would do.

For:

12cot^{2}(2x)=4

(8 exact answers)

This is my work, but its not right:

cot^{2}(2x)=1/3

cot^{2}(x)=1/3 (I changed 2x to x so that it would be easier, later I divide my answers by 2)

tan^{2}x=3

tanx=+or-(squareroot(3))

tanx= (sin(sqroot(3)/2)) / cos(1/2) (this is where I divide by 2 because I made 2x -> x above)

So i get answers of +or- pi/3, 2pi/3, 5pi/3 which obviously isn't 8 answers...

Then for:

3cos^{2}(3x)=2sin(3x)

(6 decimal answers)

I know how to start it by changing 3cos to 3 - 3sin using one of the pythag theories

but after that I am pretty much clueless

However on this one:

cos(3x)=sec(3x)+2tan^{2}(3x)

(6 exact answers) hint(get all cosines) <- teacher wrote that (however someone told me that sec may be easier)

I am clueless on how to start it, which is the main problem. For most of these problems all I need is alittle help on how to start them.

Then on the ones that I need to prove by working on one side only:

sin^{3}(x) / 1-cosx = sinx*cosx+sinx

and

(sinx / cosx-1) + (sinx / cosx+1) = 2cosx / -sinx

I only need a little help on how to start them or on how to go about solving them. As I said above I already solved a few of these on the paper, only I can't seem to grasp on how to start these specific ones.

Any help at all is appreciated and if anything is confusing please post and I will answers it ASAP.

Thanks in advance,

xhanger

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# Homework Help: Pythagorean Identities and Equations

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