How do you find the exact functional value cos 15 using the cosine sum or difference identity?

Question

17992 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-27T22:54:39

#color(red)(cos(15) = (1+ sqrt3)/(2sqrt2))#

#cos(15)= cos(45-30)#

The cosine difference identity is:

#cos(A-B) = cosAcosB+sinAsinB#

∴ #cos(15) = cos(45)cos(30) + sin(45)sin(30)#

We can use the unit circle to work out the values.

#cos(15) = sqrt2/2·sqrt3/2 + sqrt 2/2·1/2#

#cos(15)= sqrt2/4(sqrt3+1)#

#cos(15) = (1+ sqrt3)/(2sqrt2)#