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Homework Statement
Prove that sin^{6} + cos^{6} = 1 - 3sin^{2}cos^{2}
Homework Equations
(1)
The Attempt at a Solution
I tried to convert those all in terms of sine and cosine only but it didn't work.
Notice that [itex]\sin^6x=\left(\sin^2x\right)^3[/itex] and that [itex]\sin^2x=1-\cos^2x[/itex]Homework Statement
Prove that sin^{6} + cos^{6} = 1 - 3sin^{2}cos^{2}
Homework Equations
(1)
The Attempt at a Solution
I tried to convert those all in terms of sine and cosine only but it didn't work.
Every step is mathematically equivalent to its preceding step (so you haven't broken any rules) so yes, it's rightThis is my work. Is this right?
I'd also skip this line altogether (unless it's to help you to personally keep track of things and not get confused), but if not, you should just go ahead and factorize straight away:1 - 3cos^{2}x + 3(cos^{2}x)(cos^{2}x) = RHS
Also this last line is unnecessary, but there's no harm done if you feel like doing it.1 - 3cos^{2}x(sin^{2}x) = RHS
1 - 3cos^{2}xsin^{2}x = 1 - 3sin^{2}xcos^{2}x
You're welcome and that's glad to hear!Thank you!:) Now I know why my teachers hate my solutions :P I'll take note of everything you've said. God bless! Hope you could help more people like me:) I'm starting to love this forum! :D