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

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Answer 1 · 2015-08-27T22:19:30

#color(red)(sin(75) = (1+sqrt3)/(2sqrt2))#

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

The sine sum identity is:

#sin(A+B) = sinAcosB+cosAsinB#

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

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

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

#sin(75) = sqrt2/2·sqrt3/2 + sqrt2/2·1/2 = sqrt2/4(sqrt3+1)#

#sin(75) = (1+sqrt3)/(2sqrt2)#