HSC 2012 Maths Marathon (archive) (1 Viewer)

zeebobDD · Sep 23, 2012

Re: 2U Maths marathon

new q:
prove that d/ dx(Ln(x). sqrt(cosx)) = (1-sin^2(x)/ cosx^3/2 ) - [x Ln(x) tanx sqrt(cosx)] / 2

Carrotsticks · Sep 23, 2012

Re: 2U Maths marathon

Shadowdude said:
$1 + \tan^{2}{x} = \sec^{2}{x}$

Use $tan(x) = \frac{sin(x)}{cos(x)}$

That should make you be able to do it yourself.

Alternatively, you could recognise that it's in the t-formula form for sin(x), so the answer is simply sin(2x).

twinklegal19 · Sep 23, 2012

Re: 2U Maths marathon

Carrotsticks said:
Alternatively, you could recognise that it's in the t-formula form for sin(x), so the answer is simply sin(2x).

it's 2U

so they probably only need it in 2sinxcosx?

hamster-lol · Sep 27, 2012

Re: 2U Maths marathon

solve for x, sinx + cosx + tanx = 1

Sy123 · Sep 27, 2012

Re: 2U Maths marathon

For what given domain? This is 2U

Because by observation I can say x=0 is a solution.

hamster-lol · Sep 27, 2012

Re: 2U Maths marathon

Sy123 said:
For what given domain? This is 2U

Because by observation I can say x=0 is a solution.

-2pi < x < 2pi