Momo's Spech Hw help trend !

[Momo.05]

Here is the exact question from the sheet

Prove that cos(2A) = (1 - tan^2(A))/(1 + tan^2(A)) , and hence find exact values of:

a. tan(pie/12)
b. tan (pie/8)

[Momo.05]

OHH smart, yup i shall try that right after i finish this other question of mine
Thanks!

[Momo.05]

Hey.. wait..isnt tan(pie/2) undef?

[hyperblade01]

Not too sure about the hence part, but what I would do is start off with the double angle formula



We know - transpose, use quadratic formula etc


EDIT: Actually..i just realised its similar to what i've just done

Start off with:

[Momo.05]

Umm, i know its late.. But i have an issue where i cant sleep until i fully get a problem i started on.. so i was hoping you can show me the full working out to this question please? If you dont mind that is.

[hyperblade01]

Use the quadratic formula, taking the positive solution - b = 0 so i'll omit it








Rationalise denominator..






EDIT: I know you did ask for full working but I'm also tired  :buck2: gotta wake up early tomorrow >.>

[Momo.05]

wait... why cos?

[Momo.05]

nevermind
Im a bit lala ish... i missed read it ahaha

[Momo.05]

Ahh, i got a feeling this forum is likely to be my second home now ...

Any how, im back, but this time with another question which i hope i can get help on lol

Find the value of a for which there are infinitely many solutions to the equations

2x + ay - z = 0
3x + 4y - (a+1)z = 13
10x + 8y + (a-4)z = 26

-> can someone here explain to me the meaning of "infinitely many solutions" please?

Also, after finding the value of a from above, solve the equations.

Thank you very much in advance for the help, just in case i forget to thank you

[Momo.05]

Ohh this topic is matrices if that helps with the solution

[the.watchman]

For infinite many solutions graphically, the 'lines' or whatever have to be the same (think of y1=x and y2=x, if simultaneous, they have infinite sols)

(Lame answer, I know...)

[Mao]

Ahh, i got a feeling this forum is likely to be my second home now ...

Any how, im back, but this time with another question which i hope i can get help on lol

Find the value of a for which there are infinitely many solutions to the equations

2x + ay - z = 0
3x + 4y - (a+1)z = 13
10x + 8y + (a-4)z = 26

-> can someone here explain to me the meaning of "infinitely many solutions" please?

Also, after finding the value of a from above, solve the equations.

Thank you very much in advance for the help, just in case i forget to thank you

I'm pretty sure this is not part of the specialist syllabus [because it's a 3x3 system, the interpretation is a little more complicated]. So here's some reading materials if you are interested:

Visual representation of unique, none and infinite case for a 3x3 system:
http://www.mathwarehouse.com/algebra/planes/systems/three-variable-equations.php

Systematic technique of solving linear equations:
http://www.sosmath.com/matrix/system1/system1.html

Infinite solutions using Gaussian Elimination:
http://www.math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/gauss/gauss.html

But I'd recommend not really worrying about it that much.

[the.watchman]

Just wondering, is it possible to use Laplace expansion to work out when the system of equations has none or infinite solutions in this situation?

[Momo.05]

OHH right, this is methods.. !
Oopsssssssssssssssss ahaha my bad !

[Mao]

Just wondering, is it possible to use Laplace expansion to work out when the system of equations has none or infinite solutions in this situation?

Yes, you can. In SM, you are welcome to use methods beyond the syllabus, so long as you get to the right answer via a correct method.

However, Laplace expansion [i.e. determinant] does not give information about whether the system has no solutions or infinite solutions. It simply states 'unique solution' or 'no unique solutions'. Gaussian elimination is still a far better choice.