My Math Forum How $3sin^3 \theta cos^3\theta$ obtained?
 User Name Remember Me? Password

 Trigonometry Trigonometry Math Forum

 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
Math Team

Joined: May 2013
From: The Astral plane

Posts: 2,256
Thanks: 926

Math Focus: Wibbly wobbly timey-wimey stuff.
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 Display Modes Linear 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

 Contact - Home - Forums - Cryptocurrency Forum - Top