Question #2cb46

1 Answer
Jun 18, 2016

Applying identity

SinAcosB +cosAsinB=sin(A+B)

If we put A =11pi/4 and B= 2pi/3 "in the identity we get"

Sin(11pi/4)cos(2pi/3)+cos(11pi/4)sin(2pi/3)=sin(11pi/4+2pi/3)

=sin((41pi)/12)=sin(3pi+(5pi)/12)=-sin((5pi)/12)

=-sqrt(1/2(1-cos((5pi)/6))

=-sqrt(1/2(1-cos(pi-pi/6))

=-sqrt(1/2(1+cos(pi/6))

=-sqrt(1/2(1+sqrt3/2)

=-sqrt(1/8(4+2sqrt3)

=-sqrt(1/8(sqrt3+1)^2

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