How do you use a double angle formula to rewrite the expression cos2/3x?

1 Answer
Dean R.
May 1, 2018

#cos(2/3 x) = cos(2 (x/3) ) = 2 cos^2(x/3) -1 #

Explanation:

I'll assume that's

#cos(2/3 x)#

not that the other way is that different.

There are several double angle formulas for cosine. The preferred one is usually

#cos(2 theta) = 2 cos^2 theta - 1 #

#cos(2/3 x) = cos(2 (x/3) ) = 2 cos^2(x/3) -1 #

There's no good "third angle formula" like there is a half angle formula. There would be if it was possible to trisect a general angle with straightedge and compass, but it isn't.

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