Melody

Hello, i tried to prove the following trigonometric problem from a textbook but i think the equation doesn't hold. Can anyone confirm it?

So the domain of the angle is 3π/2 < x < 2π , and the equation is:

sqrt((1+cos(x))/(1-cos(x)))+sqrt((1-cos(x))/(1+cos(x))) = -2cot(x)

First I need to work out your backets.  Some spacing woud have been nice.

sqrt (  [1+cos(x)]    /  [1-cos(x)] )      +   sqrt(  [1-cos(x)]  / [1+cos(x)] ) = -2cot(x)

\(\sqrt\frac{1+cos(x)}{1-cos(x)}+\sqrt{\frac{1-cos(x)}{1+cos(x)}} = -2cot(x)\)

Is this what you are asking us to try and prove?

Here are the 2 graphs, you can see that they are not the same.  Not even in the given domain.

You have not proof read the question either.   A group of  howmany canditades?  A number is missing.

I agree with BiulderBoi.  

\(\left(1 - \frac12 \right) \cdot \left(1 - \frac13 \right) \cdot \left(1 - \frac14\right) \dotsm \left(1 - \frac {1}{2009} \right) \\=\left(\frac{1}{2}\right) \cdot \left(\frac{2}{3} \right) \cdot \left(\frac{3}{4}\right) \dotsm \left(\frac{2008}{2009} \right) \\=\frac{1}{2009}\)

The rest cancels out.

1000/19 =52 and a bit

9999/19=526 and a bit

abba  9*10 = 90 Possible palindromes.

1881, 3553, 5225, and one more. I will let you find it.

I looked at algebraic ways to do it but altimately it was just as easy (for me) to look at the possibilites prettuy much one by one.

One question per post, thanks.

Nathan starts with N toys 

Which means that Ricky starts with 3N toys

3N-k = 8        N+k=8

Solve simultaneously.

\((x+1)^2+(y-4)^2=4\)

700

or

12732

any number where the 7 is in the hundreds column.