How do you express sin(pi/ 4 ) * sin( ( 23 pi) / 12 ) sin(π4)sin(23π12) without using products of trigonometric functions?

1 Answer
May 26, 2016

-(sqrt3-1)/4314

Explanation:

sin(pi/4)*sin((23pi)/12)sin(π4)sin(23π12)

=sin(pi/4)*sin(2pi-pi/12)=sin(π4)sin(2ππ12)

=-sin(pi/4)*sin(pi/12)=sin(π4)sin(π12)

=-sin(pi/4)*sqrt(1/2(1-cos(pi/6)=sin(π4)12(1cos(π6)

=-1/sqrt2*sqrt(1/2(1-sqrt3/2))=12 12(132)

=-1/sqrt2*sqrt(1/8(4-2sqrt3))=1218(423)

=-1/4(sqrt((sqrt3-1)^2))=14((31)2)

=-1/4(sqrt3-1)=14(31)