SOLUTION: prove the following equation is an identity. show your work sin5x+sin3x=4sin2xcos2xcosx first i did the regular formula sinA+sinB=2sin(a+b/2)cos(a-b/2) so it came out like this

Question 21631: prove the following equation is an identity. show your work
sin5x+sin3x=4sin2xcos2xcosx
first i did the regular formula sinA+sinB=2sin(a+b/2)cos(a-b/2) so it came out like this : 2sin4xcosx and now i'm stuck and i dont know where to go from that can anyone help? thanks
-kt
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
YOU ALMOST GOT THE ANSWER..JUST A LITTLE FINISHING TOUCH IS NEEDED..SEE BELOW
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sin5x+sin3x=4sin2xcos2xcosx
first i did the regular formula sinA+sinB=2sin(a+b/2)cos(a-b/2)...VERY GOOD
so it came out like this : 2sin4xcosx......VERY GOOD
and now i'm stuck and i dont know where to go from that ........WHAT IS THE PROBLEM NOW SEE THE ANSWER AND DO ..WE HAVE COS X WHICH IS OK ..BUT WE HAVE SIN 4X AGAINST SIN 2X COS 2X.....HOPE YOU KNOW THE FORMULA SIN 2X=2 SIN X*COS X
IT IS DERIVED FROM SIN(A+B)=SIN A*COS B+COS A*SIN B..BY PUTTING A=B..
SO WE GET SIN 4X=SIN 2*(2X)=2*SIN 2X*COS 2X....HENCE
SIN 5X+SIN 3X= 2*(SIN 2X) *(COS 2X) *(2*COS X)=4 SIN 2X COS 2X COS X
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