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 December 23rd, 2018, 06:13 AM #1 Member   Joined: Feb 2018 From: Iran Posts: 52 Thanks: 3 Limit problem How can I solve this question without using derivatives? Last edited by Elize; December 23rd, 2018 at 06:18 AM.
 December 23rd, 2018, 06:26 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra Multiply numerator and denominator by $\cos x +\sqrt{\cos 2x}$. Thanks from greg1313 and topsquark
December 24th, 2018, 07:25 AM   #3
Member

Joined: Feb 2018
From: Iran

Posts: 52
Thanks: 3

Quote:
 Originally Posted by v8archie Multiply numerator and denominator by $\cos x +\sqrt{\cos 2x}$.
I did still couldn't solve it

 December 24th, 2018, 08:37 AM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra \begin{align}(\cos x - \sqrt{\cos 2x})(\cos x + \sqrt{\cos 2x}) &= \cos^2 x - \cos 2x \\ &= \cos^2 x - (\cos^2 x - \sin^2 x) \\ &= \sin^2 x\end{align} Thanks from topsquark and Elize

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