How do you find the exact functional value cos 75 using the cosine sum or difference identity?

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Answer 1 · 2015-08-27T22:43:26

#color(red)(cos(75)=(sqrt3 – 1)/(2sqrt2))#

#cos(75) = cos(45+30)#

The cosine sum identity is

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

∴ #cos(75)=cos(45)cos(30) – sin(45)sin(30)#

We can use the Unit Circle to evaluate these functions.

![Unit Circle]( useruploads.socratic.org
(from www.algebra.com)

#cos(75)=sqrt2/2·sqrt3/2 – sqrt2/2·1/2#

#cos(75)=sqrt2/4(sqrt3 – 1)#

#cos(75)=(sqrt3 – 1)/(2sqrt2)#