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 3 years ago
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
 3 years ago
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

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Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.1please help me figure out why .. thanks.

PaxPolaris
 3 years ago
Best ResponseYou've already chosen the best response.1\[(\sin^2\beta\cos^2\beta)^2  \sin^22\beta\]\[=\left[ (\sin^2\beta+\cos^2\beta)^24\sin^2\beta \cos^2\beta \right]  \sin^22\beta\] \[\because \left( ab \right)^2=\left( a+b \right)^24ab\]

PaxPolaris
 3 years ago
Best ResponseYou've already chosen the best response.1\[=\left[ (1)^2\left( 2\sin \beta \cos \beta \right)^2 \right]  \sin^22\beta\]\[=\left[ 1\sin^2\left( 2 \beta \right) \right]  \sin^2(2\beta)\]

PaxPolaris
 3 years ago
Best ResponseYou've already chosen the best response.1\[=\left[ \cos^2\left( 2\beta \right) \right]\sin^2(2\beta)\]\[=\cos(4\beta)\]

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.1WOW 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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