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 February 3rd, 2015, 01:28 AM #1 Member   Joined: Jul 2014 From: Seattle Posts: 96 Thanks: 2 Simplification Hello, Wolfram Alpha says: $\frac{4\tan 4x\sec 4x}{2\sqrt{\sec 4x}}=2\sin 4x{{\sec }^{\frac{3}{2}}}4x$ I obviously see that 4/2 = 2 but after that I'm just not sure. Can anyone help me out? Last edited by 3uler; February 3rd, 2015 at 01:30 AM. February 3rd, 2015, 03:08 AM   #2
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Quote:
 Originally Posted by 3uler $\frac{4\tan 4x\sec 4x}{2\sqrt{\sec 4x}}=2\sin 4x{{\sec }^{\frac{3}{2}}}4x$

$\displaystyle \frac{4\tan 4x\sec 4x}{2\sqrt{\sec 4x}} = \dfrac{4}{2}\cdot\ tan 4x \cdot\dfrac{\sec 4x}{\sqrt{\sec 4x}} = 2 \dfrac{\sin 4x}{\cos 4x}\cdot\dfrac{(\sqrt{\sec 4x})(\sqrt{\sec 4x})}{\sqrt{\sec 4x}}= \\\;\\ =2\sin 4x\cdot\dfrac{1}{\cos4x}\sqrt{\sec 4x} = 2\sin 4x\cdot\sec 4x\cdot\sqrt{\sec 4x}=2\sin 4x\sec 4x(\sec 4x)^{\frac{1}{2}} =2\sin 4x (\sec 4x)^{\frac{3}{2}}$ Tags simplification Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Chikis Elementary Math 2 September 11th, 2013 10:11 AM arron1990 Algebra 3 August 14th, 2012 04:50 AM Jakarta Algebra 3 August 4th, 2012 10:45 AM Salient Algebra 3 October 21st, 2008 01:17 PM arron1990 Calculus 1 December 31st, 1969 04:00 PM

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