Question

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

Answer 1

`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`