`sin(pi/12)cos(pi/4) + cos(pi/12)sin(pi/4)` Find the exact value of the expression.

You need to recognize the formula sin(a+b) = sin a*cos b + sin b*cos a. You need to put `a = pi/12` and `b = pi/4 ` , such that:

`sin(pi/12 + pi/4) = sin (pi/12 ) *cos (pi/4)+ sin (pi/4)cos (pi/12 )`

`sin (4pi/12)= sin (pi/12 ) *cos (pi/4)+ sin (pi/4)cos (pi/12)`

`sin (pi/3) = sin (pi/12 ) *cos (pi/4)+ sin (pi/4)cos (pi/12)`

`sin (pi/12 ) *cos (pi/4)+ sin (pi/4)cos (pi/12) = sqrt3/2`

Hence,...

You need to recognize the formula sin(a+b) = sin a*cos b + sin b*cos a. You need to put `a = pi/12` and `b = pi/4 ` , such that:

`sin(pi/12 + pi/4) = sin (pi/12 ) *cos (pi/4)+ sin (pi/4)cos (pi/12 )`

`sin (4pi/12)= sin (pi/12 ) *cos (pi/4)+ sin (pi/4)cos (pi/12)`

`sin (pi/3) = sin (pi/12 ) *cos (pi/4)+ sin (pi/4)cos (pi/12)`

`sin (pi/12 ) *cos (pi/4)+ sin (pi/4)cos (pi/12) = sqrt3/2`

Hence, the given expression could be evaluated as the sine of the sum of angles `pi/12` and `pi/4,` such that `sin (pi/3) = sin (pi/12 ) *cos (pi/4)+ sin (pi/4)cos (pi/12) = sqrt3/2`