Question

Calculus help again!

Answer 1

and here we are

Answer 2

calc 3?

Answer 3

@iambatman

Answer 4

\[\LARGE y= \tan^{-1} (\frac{1+x}{1-x}_\]
Prove that :
\[\Large y_n=(-1)^{n-1}(n-1)! \sin ^n \theta \sin n \theta \]
where theta=cot^-1 x

Answer 5

\[\LARGE y= \tan^{-1} (\frac{1+x}{1-x})\]

Answer 6

inverse?

Answer 7

so we are talking about arctan

Answer 8

My attempt..
\[\LARGE y = \frac{\pi}{2} - \cot^{-1}\cot(\frac{\pi}{4}-x)\]
\[\LARGE y = (\frac{\pi}{4}-\cot \theta)\]
\[\Large y_1 = - cosec^2 \theta\]
\[\Large y_2 = -2cosec \theta cosec \theta \cot \theta\]
can't find the pattern

Answer 9

laughing out loud

Answer 10

:|

Answer 11

you have two cosec that's a pattern to watch out for laughing out loud

Answer 12

but the required pattern is
\[\Large y_n=(-1)^{n-1}(n-1)! \sin ^n \theta \sin n \theta\]

Answer 13

whip out your book

Answer 14

If I put n=2 I get
\[\Large y_2=(-1) \sin ^2 \theta \sin 2\theta\]

Answer 15

thats kind of contradicting :s

Answer 16

when proving, don't you have to start with definition?

Answer 17

another approach