SOLVED Identity help.

Jul 2010
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I am ABSOLUTLY stuck on this idenity problem! Anyone please help!


Prove algebraically that the equation is an identity:

(5cosC-2sinC)^2+(2cosC+5sinC)^2=29

(Worried)

Please help! Thank you so much!
 
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Ackbeet

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Jun 2010
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I would probably multiply it out, and use \(\displaystyle \sin^{2}(C)+\cos^{2}(C)=1\) a few times.
 
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masters

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Jan 2008
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I am ABSOLUTLY stuck on this idenity problem! Anyone please help!



(Worried)(Worried)(Worried)

Please help! Thank you so much!
Hi wiseguy,

\(\displaystyle (5 \cos C - 2 \sin C)^2+(2 \cos C+5 \sin C)^2=29\)

\(\displaystyle 25\cos^2 C-20 \cos C \sin C+4 \sin^2 C + (4\cos^2 C+20 \cos C \sin C+ 25 \sin^2 C)=29\)

\(\displaystyle 29 \cos^2 C+29 \sin^2 C=29\)

\(\displaystyle 29(\cos^2 C+\sin^2 C)=29\)

\(\displaystyle 29(1)=29\)

\(\displaystyle 29=29\)
 
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