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 April 28th, 2018, 06:39 PM #1 Senior Member   Joined: Aug 2014 From: India Posts: 458 Thanks: 1 How $3sin^3 \theta cos^3\theta$ obtained? $15 (\sin^4X + \cos^4X) - 10 (\sin^6X - \cos^6X) = ?$ $\rightarrow 15 (1-2 \sin^2 \theta. \cos^2\theta) - (1-3\sin^3 \theta \cos^3\theta)$ $\rightarrow 15 - 30 \sin^2 \theta. \cos^2\theta - 10 + 30 \sin^2 \theta. \cos^2\theta$ $\rightarrow 15-10 = 5$ How $3\sin^3 \theta \cos^3\theta$ obtained? Last edited by skipjack; April 28th, 2018 at 08:01 PM. April 28th, 2018, 08:16 PM   #2
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Quote:
 Originally Posted by Ganesh Ujwal How $3\sin^3 \theta \cos^3\theta$ obtained?
You are likely running into trouble because it isn't true.

-Dan April 28th, 2018, 08:20 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra I suspect that you have a typo. \begin{align*} \sin^6{\theta} + \cos^6{\theta} &= (\sin^2{\theta} + \cos^2{\theta})^3 - 3\sin^2{\theta}\cos^4{\theta} - 3\sin^4{\theta}\cos^2{\theta} \\ &= 1 - 3\sin^2{\theta}\cos^2{\theta}(1-\sin^2{\theta}) - 3\sin^4{\theta}\cos^2{\theta} \\ &= 1 - 3\sin^2{\theta}\cos^2{\theta} + 3\sin^4{\theta}\cos^2{\theta} - 3\sin^4{\theta}\cos^2{\theta} \\ &= 1 - 3\sin^2{\theta}\cos^2{\theta} \end{align*} Thanks from topsquark April 28th, 2018, 08:46 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2202 \begin{align*} 10(\sin^6{\theta} + \cos^6{\theta}) &= 10(\sin^2{\theta} + \cos^2{\theta})^3 - 3\sin^4{\theta}\cos^2{\theta} - 3\sin^2{\theta}\cos^4{\theta}) \\ &= 10(1 - 3\sin^2{\theta}\cos^2{\theta}(\sin^2{\theta} + \cos^2{\theta})) \\ &= 10(1 - 3\sin^2{\theta}\cos^2{\theta}) \end{align*} Thus there were two typos: a second "-" instead of "+" in the first line of the original post, and omission of "10" in the second line. Thanks from topsquark April 29th, 2018, 05:08 AM #5 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra And the exponents in the second line make 4. Thanks from topsquark Tags $3sin3, cos3theta$, obtained, theta 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 wirewolf Trigonometry 4 March 1st, 2016 11:23 AM SourPatchKid Complex Analysis 0 April 21st, 2015 04:15 PM mared Geometry 1 June 15th, 2014 09:49 AM mauro125 Algebra 3 February 22nd, 2014 04:57 PM FelisCanisOfCadog Algebra 4 March 6th, 2009 08:05 PM

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