Question

How do you find the exact value of `cos15`using the half-angle identity?

Answer 1

Solution

`cos 30^0 = sqrt(3)/2`
`cos(2*15^0)=sqrt(3)/2`
`2cos^2(15^0)-1=sqrt(3)/2`
`2cos^2(15^0)=(sqrt(3)+2)/2`
`cos^2(15^0)=(sqrt(3)+2)/4`
`cos(15^0)=sqrt((sqrt(3)+2))/2`