Question

Use a double-angle identity to find the exact value of the trigonometric expression.

cos 420°

Answer 1

Well you can think about this two ways. The first is to use the double angle identity.

\[\cos (2a) = \cos^2(a) - \sin^2(a)\]

this means that.

\[\cos(420) = \cos^2(210) - \sin^2(210) \]

the second way is to simply realize that 420º is simply 360 + 60 and so you can reduce the problem to cos(60º) which is much easier in my opinion but I suppose the problem is very specific in the way you have to solve it.