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C3 help

Semaphore

By expressing
cos3a = 2a+a , show that ,
cos3a=4cos^3a-cosa

Im really stuck

Reply 1

username2028267

Original post by Semaphore

By expressing
cos3a = 2a+a , show that ,
cos3a=4cos^3a-cosa

Im really stuck

Try using cosine formulae.

(edited 8 years ago)

Reply 2

Semaphore

Original post by Azhar Rana

Try using cos(a+b).

So
cos(2a+a) = 4cos^3a - cosa

What to do next?:/

Reply 3

username2028267

replace cos(2α + α) with cos(2α)cos(α) – sin(2α)sin(α).

Reply 4

Blablalb

$Cos(A+B)=cosAcosB-sinAsinB$
Try that, however i do not want to tell you all of the information but obviously you've already done 1/3 of the work in the way you expressed cos(3x) as cos(2x+x)
Also note the formula for
$Sin(2A)=2sinAcosA$
$Cos(2A)=Cos^2(A)-Sin^2(A)$

(edited 8 years ago)

Reply 5

davros

Original post by Semaphore

So
cos(2a+a) = 4cos^3a - cosa

What to do next?:/

That's what you're supposed to be showing!

If you know the formula for cos(A + B) then put A = 2a and B = a into the formula and then rearrange using a standard identity that links cos^2 x and sin^2 x :smile: