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

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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)#