SOLUTION: Prove cos 3(theta) = 4 cos^3 (theta) - 3cos (theta)

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Question 1142052: Prove cos 3(theta) = 4 cos^3 (theta) - 3cos (theta)
Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
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            This problem is to be solved in 2 easy steps.


Step 1 

cos(2a) = cos(a + a) = cos(a)*cos(a) - sin(a)*sin(a) = cos^2(a) - sin^2(a) = cos^2(a) - (1-cos^2(a)) = 2*cos^2(a) - 1.


Step 2 

cos(3a) = cos(2a + a) = cos(2a)*cos(a) - sin(2a)*sin(a) = (2cos^2(a)-1)*cos(a) - (2*sin(a)*cos(a))*sin(a) = 

                      = 2*cos^3(a) - cos(a) - 2*sin^2(a)*cos(a) = 2*cos^3(a) - cos(a) - 2*(1-cos^2(a))*cos(a) = 

                      = 2*cos^3(a) - cos(a) - 2*cos(a) + 2*cos^2(a) = 4*cos^3(a) - 3*cos(a).


It is what has to be proved.