How do you prove #cos36*cos72=1/4#?
1 Answer
Assuming you do not already know the values of the two cosines, you can find both the difference and the product using the double-angle and sum-product relations for cosine. See the explanation.
Explanation:
First you should prove that
To do this let
Apply trigonometric identities you should know. From the double angle formula for cosine:
Then from the sum-product relation for cosines:
Put these results together to get:
Thus
This has two roots
Now the product is immediately known because we already calculated:
So