Question

Use a sum or difference formula to find the exact value of the trigonometric function. sine startfraction 7 pi over 12 endfractionsin 7π 12

Answer 1

we have that
sin (7π/12)=?

we know that
7π/12=(π/4+π/3)
and 
sin(A+B)=sin(A)cos(B)+cos(A)sin(B)

then
sin(π/4+π/3)=sin(π/4)cos(π/3)+cos(π/4)sin(π/3)
sin(π/4+π/3)=(√2/2)(1/2)+(√2/2)(√3/2)-------> (√2/4)+(√6/4)---> (√2+√6)/4

the answer is (√2+√6)/4