How do you find the exact value of cos( 2 arctan (5/12) )cos(2arctan(512))?
1 Answer
Jun 8, 2016
Explanation:
Use the cosine double angle formula:
cos(2x)=2cos^2(x)-1cos(2x)=2cos2(x)−1
Here, inside the cosine function, the angle
cos(2arctan(5/12))=2cos^2(arctan(5/12))-1cos(2arctan(512))=2cos2(arctan(512))−1
To find
In this triangle,
So we see that
2cos^2(arctan(5/12))-1=2(12/13)^2-1=288/169-1=119/1692cos2(arctan(512))−1=2(1213)2−1=288169−1=119169