anonymous
  • anonymous
prove this is right with identities: (sin a)^4 + (cos a)^4 = 1 - 2 * (sin a)^2 * (cos a)^2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\sin ^{4}\alpha + \cos ^{4}\alpha = 1-2 \sin ^{2}\alpha \cos ^{2}\alpha\] please help
hartnn
  • hartnn
add and subtract 2 * (sin a)^2 * (cos a)^2 on left side : (sin a)^4 + (cos a)^4
hartnn
  • hartnn
=[(sin a)^4 + (cos a)^4+2 * (sin a)^2 * (cos a)^2]-2 * (sin a)^2 * (cos a)^2 did you get what i did ?

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anonymous
  • anonymous
trying to... :) thank you...
hartnn
  • hartnn
then notice that\( (\sin a)^4 =(\sin^2a)^2 \) same for cos^4 a and that [(sin a)^4 + (cos a)^4+2 * (sin a)^2 * (cos a)^2] is of the form \(x^2+y^2+2xy=(x+y)^2\)
hartnn
  • hartnn
are u getting any of this ? please interact and ask doubts....
anonymous
  • anonymous
i'm writing it down and trying to get to eah of your steps by myself so it takes some times...thank u man :)
hartnn
  • hartnn
good :) also think of next steps...
anonymous
  • anonymous
okay, got it... sin^2a + cos^2a = 1 1^2=1 you're awesome :) thanks alot
hartnn
  • hartnn
welcome ^_^ thanks for the compliment :)

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