Question #2cb46

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Answer 1 · 2016-06-18T03:03:45

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)#