anonymous
  • anonymous
which expression is equivalent to \[(\sin^2\beta-\cos^2\beta)^2 - \sin^22\beta\]? 1.-2sin^2beta 2. 2sin^2 2beta 3. -cos4beta 4. cos4beta and the answer is 4. but again, i don't know why
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
please help me figure out why .. thanks.
PaxPolaris
  • PaxPolaris
\[(\sin^2\beta-\cos^2\beta)^2 - \sin^22\beta\]\[=\left[ (\sin^2\beta+\cos^2\beta)^2-4\sin^2\beta \cos^2\beta \right] - \sin^22\beta\] \[\because \left( a-b \right)^2=\left( a+b \right)^2-4ab\]
PaxPolaris
  • PaxPolaris
\[=\left[ (1)^2-\left( 2\sin \beta \cos \beta \right)^2 \right] - \sin^22\beta\]\[=\left[ 1-\sin^2\left( 2 \beta \right) \right] - \sin^2(2\beta)\]

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PaxPolaris
  • PaxPolaris
\[=\left[ \cos^2\left( 2\beta \right) \right]-\sin^2(2\beta)\]\[=\cos(4\beta)\]
anonymous
  • anonymous
WOW You are brilliant!!! Hahaha, I keep going back to your steps and I am still on a way to figure out how you got that... but that really helps me alot! thanks!!!!!

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