What is the exact value of #sin (45 + 30)#?

1 Answer
Andrea S.
Mar 12, 2018

#sin(45°+30°) = (sqrt2(sqrt3+1))/4 #

Explanation:

Using the formula for the sine of the sum of two angles:

#sin(alpha+beta) = sin alpha cos beta + cos alpha sin beta#

and assuming the angles are expressed in degrees:

#sin(45°+30°) = sin 45° cos 30° + cos 45°sin 30°#

#sin(45°+30°) = sqrt2/2 * sqrt3/2 + sqrt2/2 * 1/2#

#sin(45°+30°) = (sqrt2(sqrt3+1))/4 #

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