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 December 11th, 2018, 10:20 AM #1 Newbie   Joined: Dec 2018 From: Canada Posts: 14 Thanks: 0 Math Focus: mainly algebra Show that A and B are constant Any help with that if you have some free time ? Show that A and B are constant A = sin6(x) + cos6(x) + 3sin2(x).cos2(x) B= 2sin4(x) - cos4(x) - 2sin2(x) December 11th, 2018, 10:54 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,574 Thanks: 1420 I'm assuming this means $A = \sin^6(x) + \cos^6(x) + 3\sin^2(x)\cos^2(x)$ $B = 2\sin^4(x)-\cos^4(x) - 2\sin^2(x)$ as written $A+B = \sin^4(x)$ is not constant. did you mean $B = \sin^4(x)-\cos^4(x) - 2\sin^2(x)$ Thanks from topsquark December 11th, 2018, 11:00 AM #3 Global Moderator   Joined: Dec 2006 Posts: 21,019 Thanks: 2253 \displaystyle \begin{align*}A &= \sin^6(x) + \cos^6(x) + 3\sin^2(x)\cos^2(x) \\ &= \sin^6(x) + \cos^6(x) + 3\sin^2(x)\cos^2(x)(\sin^2(x) + \cos^2(x)) \\ &= (\sin^2(x) + \cos^2(x))^3 \\ &= 1\end{align*} Thanks from SkyCod December 11th, 2018, 11:15 AM   #4
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Quote:
 Originally Posted by romsek I'm assuming this means $A = \sin^6(x) + \cos^6(x) + 3\sin^2(x)\cos^2(x)$ $B = 2\sin^4(x)-\cos^4(x) - 2\sin^2(x)$ as written $A+B = \sin^4(x)$ is not constant. did you mean $B = \sin^4(x)-\cos^4(x) - 2\sin^2(x)$
No, I wrote it the right way, and I should drag out the possibility that it's wrong.

Last edited by skipjack; December 11th, 2018 at 11:50 AM. December 11th, 2018, 11:49 AM #5 Global Moderator   Joined: Dec 2006 Posts: 21,019 Thanks: 2253 \displaystyle \begin{align*}B &=2\sin^4(x) - \cos^4(x) - 2\sin^2(x) \\ &= \sin^4(x) + (\sin^2(x) + \cos^2(x))(\sin^2(x) - \cos^2(x)) - 2\sin^2(x) \\ &= \sin^4(x) + \sin^2(x) - (1 - \sin^2(x)) - 2\sin^2(x) \\ &= \sin^4(x) - 1 \end{align*} Thanks from topsquark and SkyCod Tags constant, show 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 idontknow Elementary Math 7 August 1st, 2017 12:23 PM shahbaz200 Calculus 12 December 18th, 2016 12:50 AM ag07 Complex Analysis 6 December 4th, 2015 07:05 PM JamieStarr Algebra 3 November 24th, 2010 03:18 PM notnaeem Real Analysis 4 August 16th, 2010 12:32 PM

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