Help with math problem

[Shamus]

Hi everyone,

I've just started out at uni in melbourne, and am finding it great! I have been given a set of questions to get done, and i've done most of them without any problems. but i've gotten to one which has got me stuck , and was wondering if anyone could explain how i do it.

The problem:
Simplify the following expression:

cosec^2 (x) - cot^2 (x)

If anyone can explain it to me it would be very much appreciated, thanks guys.

 

[nikopolidis]

It's simple if I correctly understand that cot(x) means ctg(x). If not then explain what do you mean be cot(x). If cot)x) = ctg(x) = cos(x)/sin(x) then solution of your problem is below...

So, let's begin...

Your problem: cosec^2(x) - cot ^2(x)
Solution: cosec^2(x) - cot ^2(x) = 1/sin^2(x) - cos^2(x)/sin^2(x) = 1/sin^2(x) - (1-sin^2(x))/sin^2(x) = 1/sin^2(x) - 1/sin^2(x) + 1 = 1

That's it!

 

[prostuff1]

It's simple if I correctly understand that cot(x) means ctg(x). If not then explain what do you mean be cot(x). If cot)x) = ctg(x) = cos(x)/sin(x) then solution of your problem is below...

So, let's begin...

Your problem: cosec^2(x) - cot ^2(x)
Solution: cosec^2(x) - cot ^2(x) = 1/sin^2(x) - cos^2(x)/sin^2(x) = 1/sin^2(x) - (1-sin^2(x))/sin^2(x) = 1/sin^2(x) - 1/sin^2(x) + 1 = 1

That's it!

The man has the right answer and if you go to wikipedia you can find the equivalents for the trig functions.

The only thing different i would have done with what nikopolidis showed was with the last step.

1 - 1 + sin^2(x) = 1
.....sin^2(x)

You should be able to understand all the step nikopolidis made but i figured i would through my 2 cents in

 

[nikopolidis]

The only thing different i would have done with what nikopolidis showed was with the last step.

Yep, thanks! Now it becomes more clear!

 

[Melrose]

I don't mean to hijack the thread, but it is math-related: Does anyone know the formula that proves the shortest distance between two points is not a straight line? I heard of this once many years ago..

 

[creator2456]

I don't mean to hijack the thread, but it is math-related: Does anyone know the formula that proves the shortest distance between two points is not a straight line? I heard of this once many years ago..

That is hard to believe, but if it can be proven, then it must be true.

To the OP, the answers above are correct.

One of my favorite 'math' problems:

girls = money x time
time = money
∴ girls = money^2
money = root of all evil
∴ girls = √evil^2

girls = evil

 

[prostuff1]

That is hard to believe, but if it can be proven, then it must be true.

To the OP, the answers above are correct.

One of my favorite 'math' problems:

girls = money x time
time = money
∴ girls = money^2
money = root of all evil
∴ girls = √evil^2

girls = evil

That is a very good math problem indeed... just don't let the girlfriend see it like mine did... they won't be impressed

 

[Gelfin]

I don't mean to hijack the thread, but it is math-related: Does anyone know the formula that proves the shortest distance between two points is not a straight line? I heard of this once many years ago..

I don't think you're going to find this because it isn't true, at least for planar Euclidean geometry. The shortest distance between two points is a straight line.

You're probably thinking of a sphere, where the shortest distance between two points is frequently curved on the 2-manifold surface. It's relevant to navigation where the shortest route between two distant points involves following a "great circle" instead of a straight line drawn on a map.

 

[Melrose]

You're probably thinking of a sphere, where the shortest distance between two points is frequently curved on the 2-manifold surface. It's relevant to navigation where the shortest route between two distant points involves following a "great circle" instead of a straight line drawn on a map.

What I'm thinking of was somehow tied in with the math Albert Einstein used in showing space is curved... but that's way out of my league to say the least That sphere thing you mentioned always confused me.

 

[iSamurai]

don't you just like maths? I'm also doing this.

here's your solution to your problem:

P.S. Images from iSight

 

[Melrose]

The funny thing is that I love math, and aced it in school. It just takes me longer than most to grasp how certain elements of it work.

One of my favourite books is The Universe and Dr Einstein, the explanation of his theories on relativity, etc. It's a good read.

Trig was not one of my specialities, alas... My dad (a tool and die machinist) is wonderful at it and loves it, even though he doesn't do that stuff anymore.