Need help with this question!!!

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• March 11th 2013, 12:12 AM
calmo11
Need help with this question arctan...
I am having trouble with this question please help
Show that arctan(x) = arccos(1/(√(1+x2)))= arcsin(x/(√(1+x2))
• March 11th 2013, 01:24 AM
Prove It
Re: Need help with this question!!!
\displaystyle \begin{align*} y &= \arctan{(x)} \\ \tan{(y)} &= x \\ \frac{\sin{(y)}}{\cos{(y)}} &= x \\ \frac{\sqrt{1 - \cos^2{(y)}}}{\cos{(y)}} &= x \\ \sqrt{1 - \cos^2{(y)}} &= x\cos{(y)} \\ 1 - \cos^2{(y)} &= x^2\cos^2{(y)} \\ 1 &= \left( 1 + x^2 \right) \cos^2{(y)} \\ \frac{1}{1 + x^2} &= \cos^2{(y)} \\ \frac{1}{\sqrt{1 + x^2}} &= \cos{(y)} \\ y &= \arccos{\left( \frac{1}{\sqrt{1 + x^2}} \right)} \end{align*}

Now follow a similar process for the second part.
• March 12th 2013, 12:54 AM
calmo11
Re: Need help with this question!!!
Thankyou very much, helped me out perfectly