find the exact value of sin 7pi12 by using a sum or differen

find the exact value of sin 7pi/12 by using a sum or difference formula

Solution

sin(7pi/12) = sin(pi/3 +pi/4)

Use sin(A+B) = sinAcosB + cosAsinB

sin(pi/3 +pi/4) = sinpi/3cospi/4 + cospi/3sinpi/4

= [sqrt(3)/2](1/sqrt2) + (1/2)1/sqrt2

= ( sqrt(3) +1)/2sqrt(2)