We can only use the sine and cosine functions of `30^"o"`, so we need to start with `60^"o" = 2 × 30^"o"`.

We will use the result

cos 2

α= cos^{2}α− sin^{2}α,

and the 30-60 triangle:

Now we proceed to find the exact value of cos60° using the ratios of 30°:

`cos 60^text(o)=cos(2xx30^text(o))`

`=cos^2(30^text(o))-sin^2(30^text(o))`

`=(sqrt3/2)^2-(1/2)^2`

`=3/4-1/4`

`=2/4`

`=1/2`

These exercises are really here for practice on the double angle formula. Of course, we could have found the value of cos60° directly from the triangle.

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