Melody

I live in Australia though.  

That is why my icon is a kangaroo road sign.  It is a photo of a real road sign    

No it is not :)

Thanks for your input but I think something you should include if you are giving out advice or suggestions is cost. 

Not exact cost, you may not even know that, but just an idea of cost. 

In particular, is a resource free, relatively inexpensive or pricey.

It is of key importance to almost everyone.

8! / ( 3!3!2!)

I have shown it but I am sure I have not done it by the intended method

My method is far from elegant.

Find BD in terms of  angle BCD using the cosine rule  and also

Find BD in terms of  angle BAD using the cosine rule  

not that angle BCD and angle BAD are supplementary which means  cos

Solve for angle

Then use to find distance  BD

Do the same for AC

Then you can just substitute to show that they are the same. 

I am sure this is not quite the intended solution.

Ask questions if you want to :)

\(RHS = (cos^2x-sin^2x)*\frac{1}{cos^2x}\\\)

I am sure you can finish it.

Why would anyone want to help you?

You have asked 57 questions and never EVER said thank you for an answer.

Plus. although you have given yourself some points for asking your own questions, 

You have never given anyone a point of answering.

Steps

1)  Draw a bigger pic and put all the given info on it.

2)  Every angle there is easy to find,  find them all.

3)  consider triangle EBC

       Sin EBC = EC/12

       angle EBS = angle EBD+angle DBC

       so

       \(sin(\angle EBD+\angle DBC)=\frac{EC}{12}\)

       You will need to use the sin (A+B) formula to solve this.

Now try filling in all the blanks for yourself.

Your welcome.

And now you know 

If you had search "LaTex triangle symbol" it would have come straight up - in picture form.   :)

This function is a concave down parabola so just find the maximum point.

hint: the x value is   -b/(2a)    then sub that in to get the P value