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Re: HSC 2013 2U Marathon $Evaluate $\int_{\frac{-\pi}{4}}^0 \frac{dx}{\sqrt{cosec^2x - 1}}

Lets put the things with 'x' on one side, and the other letters on the other side ae^x = be^{-x} \\ \\ \frac{e^x}{e^{-x}}= \frac{b}{a} \\$Using indices laws, $\frac{a^m}{a^n} = a^{m-n} \\ e^{2x} = \frac{b}{a} \\ \\ 2x = log_e \left ( \frac{b}{a} \right )

oh right lol (and it he didnt differentiate aswell lol...)

c = \sqrt{1+2\sqrt{1+2\sqrt{1+2\sqrt{\dots}}}} Square both sides, noting that (\sqrt{a})^2 = a c^2 = 1+2\sqrt{1+2\sqrt{1+2\sqrt{1+2\sqrt{\dots}}}} Subtract '1' from both sides, c^2 \bold{-1} = 1+2\left ( \sqrt{1+2\sqrt{1+2\sqrt{1+2\sqrt{\dots}}}} \right ) \bold{-1} c^2 - 1 =...

mistake...

c = \sqrt{1+2\sqrt{1+2\sqrt{\dots}}} \\ \\ c^2 - 1 = 2\sqrt{1+2\sqrt{1+2\sqrt{\dots}}} \\ \\ \frac{c^2 - 1}{2} = \sqrt{1+2\sqrt{1+2\sqrt{\dots}}} \\ \\ \frac{c^2 - 1}{2} = c I hope you can follow this

Re: Chess thread? u there? http://lichess.org/bnt2kd8v

Re: Chess thread? lol i was waiting and then it went 'Game Over' :O can u host it?

Re: Chess thread? sorry this one: http://lichess.org/qsozcys0

Re: Chess thread? Ok

Re: Chess thread? .

Noice! Thanks for sharing!

I see, the dash in that phrase confused me because i thought it was a minus sign lol

Question 1 beautiful c = \sqrt{1+2\sqrt{1+2\sqrt{\dots}}} \\ \\ \frac{c^2-1}{2} = c \\ \\ c^2 - 2c - 1 = 0 By completing the square or applying the quadratic formula, solve for c

No!!! dont leave!!!! what if this exact question popped up in the HSC? then u may have lost some marks in ur 2U exam!

I am no genius, look at the denominator of the answer, there is no imaginary so you must 'realise' the denominator (like rationalising - by timing top and bot by conj) And the rest is trig identities (double/half angles) and trying to make LHS look like the RHS, by taking out the half, by...

HSC2014 and I have different answers to you and Smile12345 The share value is 97.3% of original after Monday IF share value is then reduced by 3.09% (at the end of Tuesday), then 3.09% of the remaining 97.3% of the share value is LOST! SO, then 96.91% of the share value of 97.3% is LEFT...

Assuming you know all your trig identities.... Let z = cis(theta) \rightarrow \\ = \frac{z}{1-z}\cdot \frac{\overline{1-z}}{\overline{1-z}} ($times top and bot by denom's conj$)\\ \\ = \frac{z(\overline{1}-\overline{z})}{(1-z)(\overline{1-z})} note: z . z(bar) = |z|^2 \rightarrow \\ =...

LOL! DAMN i didnt see that 'i' outside......

Have you 'realised' the denominator? (times top and bottom by the denomintor's conjugate)