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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- Jul 15th 2010, 12:16 PMwiseguyIdentity help.
I am ABSOLUTLY stuck on this idenity problem! Anyone please help!

Prove algebraically that the equation is an identity:

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

(Worried)

Please help! Thank you so much! - Jul 15th 2010, 12:31 PMAckbeet
I would probably multiply it out, and use $\displaystyle \sin^{2}(C)+\cos^{2}(C)=1$ a few times.

- Jul 15th 2010, 12:32 PMmasters
Hi wiseguy,

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

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

$\displaystyle 29 \cos^2 C+29 \sin^2 C=29$

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

$\displaystyle 29(1)=29$

$\displaystyle 29=29$ - Jul 15th 2010, 01:13 PMwiseguy
Thank you!! Duh to me! alskjd;f