How do you use the angle sum or difference identity to find the exact value of sin((5pi)/12)sin(5π12)?

1 Answer
Oct 2, 2016

sin((5pi)/12)=(1+sqrt3)/(2sqrt2)sin(5π12)=1+322

Explanation:

As sin(A+B)=sinAcosB+cosAsinBsin(A+B)=sinAcosB+cosAsinB

and (5pi)/12=(2pi+3pi)/12=(2pi)/12+(3pi)/12=pi/6+pi/45π12=2π+3π12=2π12+3π12=π6+π4

sin((5pi)/12)=sin(pi/6+pi/4)=sin(pi/6)cos(pi/4)+cos(pi/6)sin(pi/4)sin(5π12)=sin(π6+π4)=sin(π6)cos(π4)+cos(π6)sin(π4)

= 1/2xx1/sqrt2+sqrt3/2xx1/sqrt212×12+32×12

= (1+sqrt3)/(2sqrt2)1+322