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

Algebra ->  Trigonometry-basics -> 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      Log On


   

Question 21601: 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) About Me  (Show Source):
You can put this solution on YOUR website!
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prove the following equation is an identity. show your work
sin5x+sin3x=4sin2xcos2xcosx....OK
first i did the regular formula sinA+sinB=2sin(a+b/2)cos(a-b/2)....GOOD
so it came out like this : 2sin4xcosx .........VERY GOOD ..CONTINUE THE SAME WAY
THE KEY IS YOU KNOW WHAT THE ANSWER IS..SO MANIPULATE YOUR WORKING TO LEAD THAT
WE SHOULD GET SIN 2X , COS 2X AND COS X ...WE ALREADY HAVE COS X ..WE HAVE SIN 4X WHICH WE DONT WANT SO WRITE
SIN 4X = SIN (2X+2X)....OR ......SIN 2*(2X).....USING SIN (A+B)=SIN A * COS B +COS A * SIN B = SINCE A=B HERE WE GET = 2 SIN A COS A = SIN 2A...SO
SIN 4X = 2*SIN 2X 8 COS 2X ..SO WE GET FINALLY
SIN 5X + SIN 3X = 4*SIN 2X * COS 2X * COS X