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

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Answer 1 · 2018-03-12T14:38:10

$sin(45°+30°) = (sqrt2(sqrt3+1))/4$

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:

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

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

$sin(45°+30°) = (sqrt2(sqrt3+1))/4$

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